No sigáis leyendo si no conocéis mi post anterior: "Me gusta contaminar el planeta !" e intentad resolver el acertijo !
Antes que nada os daré una pista. Normalmente para averiguar el tipo de una sucesión se hace las restas sucesivas entre los numeres, y si esto no dice nada se hace las restas del resultado. Si la primera linea de numeres es constante quiere decir que es una sucesión lineal, y si es constante la segunda es una progresión cuadrática. Por ejemplo:
4 7 12 19 28 39 52 67 84 103 124
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
3 5 7 9 11 13 15 17 19 21
\ / \ / \ / \ / \ / \ / \ / \ / \ /
2 2 2 2 2 2 2 2 2es una sucesión cuadrática.
Ya sabéis como lo hice, podéis volver a intentar resolverlo, y si no os sale continuad leyendo.
Mi sucesión la hice de manera que la cuarta linea de restas es una copia de la primera:
0 1 2 3 5 10 21 43 86 171 341 682 1365 2731 5462 \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / 1 1 1 2 5 11 22 43 85 170 341 683 1366 2731 \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / 0 0 1 3 6 11 21 42 85 171 342 683 1365 \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / 0 1 2 3 5 10 21 43 86 171 341 682
Bueno, como ya lo sabéis todo intentad sacar los primeros 1000 numeres. Mi solución viene a continuación.
| El algoritmo es muy fácil: | |||||||
| Comienza con un triángulo pequeño, copiamos el primer numero y vamos haciendo sumas. Después se repite el proceso. |
| Escrito en PERL seria: | |
#!/usr/bin/perl # use strict; use warnings; my @suc = (0, 1, 2); my $a = 2; my $b = 1; my $c = 0; for ( my $i = 0; $i < 998; $i++ ) { my $d = $suc[$i]; $c += $d; $b += $c; $a += $b; push @suc, $a; } $" = ", "; print "@suc\n"; | Donde:
|
Y el resultado de la ejecución del script es (como es muy largo los 900 numeres restantes están ocultos):
0, 1, 2, 3, 5, 10, 21, 43, 86, 171, 341, 682, 1365, 2731, 5462, 10923, 21845, 43690, 87381, 174763, 349526, 699051, 1398101, 2796202, 5592405, 11184811, 22369622, 44739243, 89478485, 178956970, 357913941, 715827883, 1431655766, 2863311531, 5726623061, 11453246122, 22906492245, 45812984491, 91625968982, 183251937963, 366503875925, 733007751850, 1466015503701, 2932031007403, 5864062014806, 11728124029611, 23456248059221, 46912496118442, 93824992236885, 187649984473771, 375299968947542, 750599937895083, 1.50119987579016e+15, 3.00239975158033e+15, 6.00479950316066e+15, 1.20095990063213e+16, 2.40191980126426e+16, 4.80383960252853e+16, 9.60767920505706e+16, 1.92153584101141e+17, 3.84307168202282e+17, 7.68614336404565e+17, 1.53722867280913e+18, 3.07445734561826e+18, 6.14891469123652e+18, 1.2297829382473e+19, 2.45956587649461e+19, 4.91913175298921e+19, 9.83826350597843e+19, 1.96765270119569e+20, 3.93530540239137e+20, 7.87061080478274e+20, 1.57412216095655e+21, 3.1482443219131e+21, 6.29648864382619e+21, 1.25929772876524e+22, 2.51859545753048e+22, 5.03719091506096e+22, 1.00743818301219e+23, 2.01487636602438e+23, 4.02975273204876e+23, 8.05950546409753e+23, 1.61190109281951e+24, 3.22380218563901e+24, 6.44760437127802e+24, 1.2895208742556e+25, 2.57904174851121e+25, 5.15808349702242e+25, 1.03161669940448e+26, 2.06323339880897e+26, 4.12646679761793e+26, 8.25293359523587e+26, 1.65058671904717e+27, 3.30117343809435e+27, 6.6023468761887e+27, 1.32046937523774e+28, 2.64093875047548e+28, 5.28187750095096e+28, 1.05637550019019e+29, 2.11275100038038e+29, 4.22550200076077e+29, 8.45100400152153e+29, 1.69020080030431e+30,
[CONTINUA]
3.38040160060861e+30, 6.76080320121722e+30, 1.35216064024344e+31, 2.70432128048689e+31, 5.40864256097378e+31, 1.08172851219476e+32,
2.16345702438951e+32, 4.32691404877902e+32, 8.65382809755805e+32, 1.73076561951161e+33, 3.46153123902322e+33, 6.92306247804644e+33,
1.38461249560929e+34, 2.76922499121858e+34, 5.53844998243715e+34, 1.10768999648743e+35, 2.21537999297486e+35, 4.43075998594972e+35,
8.86151997189944e+35, 1.77230399437989e+36, 3.54460798875978e+36, 7.08921597751955e+36, 1.41784319550391e+37, 2.83568639100782e+37,
5.67137278201564e+37, 1.13427455640313e+38, 2.26854911280626e+38, 4.53709822561251e+38, 9.07419645122503e+38, 1.81483929024501e+39,
3.62967858049001e+39, 7.25935716098002e+39, 1.451871432196e+40, 2.90374286439201e+40, 5.80748572878402e+40, 1.1614971457568e+41,
2.32299429151361e+41, 4.64598858302721e+41, 9.29197716605443e+41, 1.85839543321089e+42, 3.71679086642177e+42, 7.43358173284354e+42,
1.48671634656871e+43, 2.97343269313742e+43, 5.94686538627483e+43, 1.18937307725497e+44, 2.37874615450993e+44, 4.75749230901987e+44,
9.51498461803973e+44, 1.90299692360795e+45, 3.80599384721589e+45, 7.61198769443179e+45, 1.52239753888636e+46, 3.04479507777271e+46,
6.08959015554543e+46, 1.21791803110909e+47, 2.43583606221817e+47, 4.87167212443634e+47, 9.74334424887269e+47, 1.94866884977454e+48,
3.89733769954907e+48, 7.79467539909815e+48, 1.55893507981963e+49, 3.11787015963926e+49, 6.23574031927852e+49, 1.2471480638557e+50,
2.49429612771141e+50, 4.98859225542282e+50, 9.97718451084563e+50, 1.99543690216913e+51, 3.99087380433825e+51, 7.98174760867651e+51,
1.5963495217353e+52, 3.1926990434706e+52, 6.3853980869412e+52, 1.27707961738824e+53, 2.55415923477648e+53, 5.10831846955296e+53,
1.02166369391059e+54, 2.04332738782119e+54, 4.08665477564237e+54, 8.17330955128474e+54, 1.63466191025695e+55, 3.2693238205139e+55,
6.53864764102779e+55, 1.30772952820556e+56, 2.61545905641112e+56, 5.23091811282223e+56, 1.04618362256445e+57, 2.09236724512889e+57,
4.18473449025779e+57, 8.36946898051558e+57, 1.67389379610312e+58, 3.34778759220623e+58, 6.69557518441246e+58, 1.33911503688249e+59,
2.67823007376498e+59, 5.35646014752997e+59, 1.07129202950599e+60, 2.14258405901199e+60, 4.28516811802397e+60, 8.57033623604795e+60,
1.71406724720959e+61, 3.42813449441918e+61, 6.85626898883836e+61, 1.37125379776767e+62, 2.74250759553534e+62, 5.48501519107069e+62,
1.09700303821414e+63, 2.19400607642827e+63, 4.38801215285655e+63, 8.7760243057131e+63, 1.75520486114262e+64, 3.51040972228524e+64,
7.02081944457048e+64, 1.4041638889141e+65, 2.80832777782819e+65, 5.61665555565638e+65, 1.12333111113128e+66, 2.24666222226255e+66,
4.49332444452511e+66, 8.98664888905021e+66, 1.79732977781004e+67, 3.59465955562009e+67, 7.18931911124017e+67, 1.43786382224803e+68,
2.87572764449607e+68, 5.75145528899214e+68, 1.15029105779843e+69, 2.30058211559685e+69, 4.60116423119371e+69, 9.20232846238742e+69,
1.84046569247748e+70, 3.68093138495497e+70, 7.36186276990994e+70, 1.47237255398199e+71, 2.94474510796397e+71, 5.88949021592795e+71,
1.17789804318559e+72, 2.35579608637118e+72, 4.71159217274236e+72, 9.42318434548472e+72, 1.88463686909694e+73, 3.76927373819389e+73,
7.53854747638777e+73, 1.50770949527755e+74, 3.01541899055511e+74, 6.03083798111022e+74, 1.20616759622204e+75, 2.41233519244409e+75,
4.82467038488818e+75, 9.64934076977635e+75, 1.92986815395527e+76, 3.85973630791054e+76, 7.71947261582108e+76, 1.54389452316422e+77,
3.08778904632843e+77, 6.17557809265686e+77, 1.23511561853137e+78, 2.47023123706275e+78, 4.94046247412549e+78, 9.88092494825098e+78,
1.9761849896502e+79, 3.95236997930039e+79, 7.90473995860079e+79, 1.58094799172016e+80, 3.16189598344031e+80, 6.32379196688063e+80,
1.26475839337613e+81, 2.52951678675225e+81, 5.0590335735045e+81, 1.0118067147009e+82, 2.0236134294018e+82, 4.0472268588036e+82, 8.09445371760721e+82,
1.61889074352144e+83, 3.23778148704288e+83, 6.47556297408576e+83, 1.29511259481715e+84, 2.59022518963431e+84, 5.18045037926861e+84,
1.03609007585372e+85, 2.07218015170744e+85, 4.14436030341489e+85, 8.28872060682978e+85, 1.65774412136596e+86, 3.31548824273191e+86,
6.63097648546382e+86, 1.32619529709276e+87, 2.65239059418553e+87, 5.30478118837106e+87, 1.06095623767421e+88, 2.12191247534842e+88,
4.24382495069685e+88, 8.48764990139369e+88, 1.69752998027874e+89, 3.39505996055748e+89, 6.79011992111495e+89, 1.35802398422299e+90,
2.71604796844598e+90, 5.43209593689196e+90, 1.08641918737839e+91, 2.17283837475679e+91, 4.34567674951357e+91, 8.69135349902714e+91,
1.73827069980543e+92, 3.47654139961086e+92, 6.95308279922171e+92, 1.39061655984434e+93, 2.78123311968869e+93, 5.56246623937737e+93,
1.11249324787547e+94, 2.22498649575095e+94, 4.4499729915019e+94, 8.89994598300379e+94, 1.77998919660076e+95, 3.55997839320152e+95,
7.11995678640303e+95, 1.42399135728061e+96, 2.84798271456121e+96, 5.69596542912243e+96, 1.13919308582449e+97, 2.27838617164897e+97,
4.55677234329794e+97, 9.11354468659588e+97, 1.82270893731918e+98, 3.64541787463835e+98, 7.29083574927671e+98, 1.45816714985534e+99,
2.91633429971068e+99, 5.83266859942137e+99, 1.16653371988427e+100, 2.33306743976855e+100, 4.66613487953709e+100, 9.33226975907419e+100,
1.86645395181484e+101, 3.73290790362967e+101, 7.46581580725935e+101, 1.49316316145187e+102, 2.98632632290374e+102, 5.97265264580748e+102,
1.1945305291615e+103, 2.38906105832299e+103, 4.77812211664598e+103, 9.55624423329197e+103, 1.91124884665839e+104, 3.82249769331679e+104,
7.64499538663357e+104, 1.52899907732671e+105, 3.05799815465343e+105, 6.11599630930686e+105, 1.22319926186137e+106, 2.44639852372274e+106,
4.89279704744549e+106, 9.78559409489097e+106, 1.95711881897819e+107, 3.91423763795639e+107, 7.82847527591278e+107, 1.56569505518256e+108,
3.13139011036511e+108, 6.26278022073022e+108, 1.25255604414604e+109, 2.50511208829209e+109, 5.01022417658418e+109, 1.00204483531684e+110,
2.00408967063367e+110, 4.00817934126734e+110, 8.01635868253468e+110, 1.60327173650694e+111, 3.20654347301387e+111, 6.41308694602775e+111,
1.28261738920555e+112, 2.5652347784111e+112, 5.1304695568222e+112, 1.02609391136444e+113, 2.05218782272888e+113, 4.10437564545776e+113,
8.20875129091552e+113, 1.6417502581831e+114, 3.28350051636621e+114, 6.56700103273241e+114, 1.31340020654648e+115, 2.62680041309297e+115,
5.25360082618593e+115, 1.05072016523719e+116, 2.10144033047437e+116, 4.20288066094874e+116, 8.40576132189749e+116, 1.6811522643795e+117,
3.362304528759e+117, 6.72460905751799e+117, 1.3449218115036e+118, 2.6898436230072e+118, 5.37968724601439e+118, 1.07593744920288e+119,
2.15187489840576e+119, 4.30374979681151e+119, 8.60749959362303e+119, 1.72149991872461e+120, 3.44299983744921e+120, 6.88599967489842e+120,
1.37719993497968e+121, 2.75439986995937e+121, 5.50879973991874e+121, 1.10175994798375e+122, 2.2035198959675e+122, 4.40703979193499e+122,
8.81407958386998e+122, 1.762815916774e+123, 3.52563183354799e+123, 7.05126366709599e+123, 1.4102527334192e+124, 2.82050546683839e+124,
5.64101093367679e+124, 1.12820218673536e+125, 2.25640437347072e+125, 4.51280874694143e+125, 9.02561749388286e+125, 1.80512349877657e+126,
3.61024699755314e+126, 7.22049399510629e+126, 1.44409879902126e+127, 2.88819759804252e+127, 5.77639519608503e+127, 1.15527903921701e+128,
2.31055807843401e+128, 4.62111615686803e+128, 9.24223231373605e+128, 1.84844646274721e+129, 3.69689292549442e+129, 7.39378585098884e+129,
1.47875717019777e+130, 2.95751434039554e+130, 5.91502868079107e+130, 1.18300573615821e+131, 2.36601147231643e+131, 4.73202294463286e+131,
9.46404588926572e+131, 1.89280917785314e+132, 3.78561835570629e+132, 7.57123671141257e+132, 1.51424734228251e+133, 3.02849468456503e+133,
6.05698936913006e+133, 1.21139787382601e+134, 2.42279574765202e+134, 4.84559149530405e+134, 9.69118299060809e+134, 1.93823659812162e+135,
3.87647319624324e+135, 7.75294639248647e+135, 1.55058927849729e+136, 3.10117855699459e+136, 6.20235711398918e+136, 1.24047142279784e+137,
2.48094284559567e+137, 4.96188569119134e+137, 9.92377138238269e+137, 1.98475427647654e+138, 3.96950855295307e+138, 7.93901710590615e+138,
1.58780342118123e+139, 3.17560684236246e+139, 6.35121368472492e+139, 1.27024273694498e+140, 2.54048547388997e+140, 5.08097094777994e+140,
1.01619418955599e+141, 2.03238837911197e+141, 4.06477675822395e+141, 8.1295535164479e+141, 1.62591070328958e+142, 3.25182140657916e+142,
6.50364281315832e+142, 1.30072856263166e+143, 2.60145712526333e+143, 5.20291425052665e+143, 1.04058285010533e+144, 2.08116570021066e+144,
4.16233140042132e+144, 8.32466280084265e+144, 1.66493256016853e+145, 3.32986512033706e+145, 6.65973024067412e+145, 1.33194604813482e+146,
2.66389209626965e+146, 5.32778419253929e+146, 1.06555683850786e+147, 2.13111367701572e+147, 4.26222735403144e+147, 8.52445470806287e+147,
1.70489094161257e+148, 3.40978188322515e+148, 6.8195637664503e+148, 1.36391275329006e+149, 2.72782550658012e+149, 5.45565101316024e+149,
1.09113020263205e+150, 2.18226040526409e+150, 4.36452081052819e+150, 8.72904162105638e+150, 1.74580832421128e+151, 3.49161664842255e+151,
6.9832332968451e+151, 1.39664665936902e+152, 2.79329331873804e+152, 5.58658663747608e+152, 1.11731732749522e+153, 2.23463465499043e+153,
4.46926930998087e+153, 8.93853861996173e+153, 1.78770772399235e+154, 3.57541544798469e+154, 7.15083089596939e+154, 1.43016617919388e+155,
2.86033235838775e+155, 5.72066471677551e+155, 1.1441329433551e+156, 2.2882658867102e+156, 4.57653177342041e+156, 9.15306354684081e+156,
1.83061270936816e+157, 3.66122541873633e+157, 7.32245083747265e+157, 1.46449016749453e+158, 2.92898033498906e+158, 5.85796066997812e+158,
1.17159213399562e+159, 2.34318426799125e+159, 4.6863685359825e+159, 9.37273707196499e+159, 1.874547414393e+160, 3.749094828786e+160,
7.49818965757199e+160, 1.4996379315144e+161, 2.9992758630288e+161, 5.9985517260576e+161, 1.19971034521152e+162, 2.39942069042304e+162,
4.79884138084608e+162, 9.59768276169215e+162, 1.91953655233843e+163, 3.83907310467686e+163, 7.67814620935372e+163, 1.53562924187074e+164,
3.07125848374149e+164, 6.14251696748298e+164, 1.2285033934966e+165, 2.45700678699319e+165, 4.91401357398638e+165, 9.82802714797277e+165,
1.96560542959455e+166, 3.93121085918911e+166, 7.86242171837821e+166, 1.57248434367564e+167, 3.14496868735128e+167, 6.28993737470257e+167,
1.25798747494051e+168, 2.51597494988103e+168, 5.03194989976206e+168, 1.00638997995241e+169, 2.01277995990482e+169, 4.02555991980964e+169,
8.05111983961929e+169, 1.61022396792386e+170, 3.22044793584772e+170, 6.44089587169543e+170, 1.28817917433909e+171, 2.57635834867817e+171,
5.15271669735635e+171, 1.03054333947127e+172, 2.06108667894254e+172, 4.12217335788508e+172, 8.24434671577015e+172, 1.64886934315403e+173,
3.29773868630806e+173, 6.59547737261612e+173, 1.31909547452322e+174, 2.63819094904645e+174, 5.2763818980929e+174, 1.05527637961858e+175,
2.11055275923716e+175, 4.22110551847432e+175, 8.44221103694864e+175, 1.68844220738973e+176, 3.37688441477945e+176, 6.75376882955891e+176,
1.35075376591178e+177, 2.70150753182356e+177, 5.40301506364713e+177, 1.08060301272943e+178, 2.16120602545885e+178, 4.3224120509177e+178,
8.6448241018354e+178, 1.72896482036708e+179, 3.45792964073416e+179, 6.91585928146832e+179, 1.38317185629366e+180, 2.76634371258733e+180,
5.53268742517466e+180, 1.10653748503493e+181, 2.21307497006986e+181, 4.42614994013973e+181, 8.85229988027945e+181, 1.77045997605589e+182,
3.54091995211178e+182, 7.08183990422356e+182, 1.41636798084471e+183, 2.83273596168942e+183, 5.66547192337885e+183, 1.13309438467577e+184,
2.26618876935154e+184, 4.53237753870308e+184, 9.06475507740616e+184, 1.81295101548123e+185, 3.62590203096246e+185, 7.25180406192493e+185,
1.45036081238499e+186, 2.90072162476997e+186, 5.80144324953994e+186, 1.16028864990799e+187, 2.32057729981598e+187, 4.64115459963195e+187,
9.28230919926391e+187, 1.85646183985278e+188, 3.71292367970556e+188, 7.42584735941113e+188, 1.48516947188223e+189, 2.97033894376445e+189,
5.9406778875289e+189, 1.18813557750578e+190, 2.37627115501156e+190, 4.75254231002312e+190, 9.50508462004624e+190, 1.90101692400925e+191,
3.8020338480185e+191, 7.60406769603699e+191, 1.5208135392074e+192, 3.0416270784148e+192, 6.08325415682959e+192, 1.21665083136592e+193,
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1.36249365130904e+295, 2.72498730261807e+295, 5.44997460523614e+295, 1.08999492104723e+296, 2.17998984209446e+296, 4.35997968418891e+296,
8.71995936837783e+296, 1.74399187367557e+297, 3.48798374735113e+297, 6.97596749470226e+297, 1.39519349894045e+298, 2.7903869978809e+298,
5.58077399576181e+298, 1.11615479915236e+299, 2.23230959830472e+299, 4.46461919660945e+299, 8.9292383932189e+299, 1.78584767864378e+300,
3.57169535728756e+300
Y ahora me voy a pensar en otras cosas.
P.D. Me da asco el editor de posts ese !!!
6 comentarios:
Borracho!
Te voy a decir como lo pensé yo
Bn=1,1,0,-1,-1,0,1,1,-1,-1,0,1,1,..
Tu sucesión es...
A(1)=0
An= 2*A(n-1)+Bn
Yo no lo veo tan complicado.
se mascapao un cero pero tu lo has visto, no?
Piensa, porque pasa esto... Tambien lo pensare.
I'm impressed with your site, very nice graphics!
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Greets to the webmaster of this wonderful site! Keep up the good work. Thanks.
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Your site is on top of my favourites - Great work I like it.
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