cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A060455 7th-order Fibonacci numbers with a(0)=...=a(6)=1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 7, 13, 25, 49, 97, 193, 385, 769, 1531, 3049, 6073, 12097, 24097, 48001, 95617, 190465, 379399, 755749, 1505425, 2998753, 5973409, 11898817, 23702017, 47213569, 94047739, 187339729, 373174033, 743349313, 1480725217
Offset: 0

Views

Author

Frank Ellermann, Apr 08 2001

Keywords

Comments

a(n) = number of runs in polyphase sort using 8 tapes and n-6 phases.

Examples

			General formula for k-th order numbers: f(n,k) = f(n-1,k) + ... + f(n-1-k,k) for n > k, otherwise f(n,k) = 1.

References

  • N. Wirth, Algorithmen und Datenstrukturen, 1975 (table 2.15 chapter 2.3.4).

Links

Crossrefs

For k=1..5 see A000045, A000213, A000288, A000322, A000383.
Cf. A253333, A253318: primes and indices of primes in this sequence.
Cf. A122189 Heptanacci numbers with a(0),...,a(6) = 0,0,0,0,0,0,1.

Programs

  • Magma
    m:=40; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(  (1-x^2-2*x^3-3*x^4-4*x^5-5*x^6)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7) )); // G. C. Greubel, Feb 03 2019
  • Maple
    A060455 := proc(n) option remember: if n >=0 and n<=6 then RETURN(1) fi: procname(n-1)+procname(n-2)+procname(n-3)+procname(n-4)+procname(n-5)+procname(n-6)+procname(n-7) end;
  • Mathematica
    LinearRecurrence[{1,1,1,1,1,1,1},{1,1,1,1,1,1,1},40] (* Harvey P. Dale, Mar 17 2012 *)
  • PARI
    Vec((1-x^2-2*x^3-3*x^4-4*x^5-5*x^6)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7) +O(x^40)) \\ Charles R Greathouse IV, Feb 03 2014
  • Sage
    ((1-x^2-2*x^3-3*x^4-4*x^5-5*x^6)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7) ).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Feb 03 2019

Formula

a(n) = a(n-1) + a(n-2) + ... + a(n-7) for n > 6, a(0)=a(1)=...=a(6)=1.
G.f.: (-1 + x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 5*x^6)/(-1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7). - R. J. Mathar, Oct 11 2011

Extensions

More terms from James Sellers, Apr 11 2001

A253333 Primes in the 7th-order Fibonacci numbers A060455.

Original entry on oeis.org

7, 13, 97, 193, 769, 1531, 3049, 6073, 12097, 24097, 95617, 379399, 2998753, 187339729, 373174033, 2949551617, 184265983633, 731152932481, 88025699967469825543, 175344042716296888429, 4979552865927484193343796114081304399449
Offset: 1

Views

Author

Robert Price, Dec 30 2014

Keywords

Comments

a(22) is too large to display here. It has 53 digits and is the 180th term in A060455.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192, A060455, A253318.

Programs

  • Mathematica
    a={1,1,1,1,1,1,1}; step=7; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,sum]]; a=RotateLeft[a]; a[[7]]=sum]; lst
With[{c=PadRight[{},7,1]},Select[LinearRecurrence[c,c,150],PrimeQ]] (* Harvey P. Dale, May 08 2015 *)
  • PARI
    lista(nn) = {gf = ( -1+x^2+2*x^3+3*x^4+4*x^5+5*x^6 ) / ( -1+x+x^2+x^3+x^4+x^5+x^6+x^7 ); for (n=0, nn, if (isprime(p=polcoeff(gf+O(x^(n+1)), n)), print1(p, ", ")););} \\ Michel Marcus, Jan 11 2015

A254413 Primes in the 8th-order Fibonacci numbers A123526.

Original entry on oeis.org

29, 113, 449, 226241, 14307889, 113783041, 1820091580429249, 233322881089059894782836851617, 29566627412209231076314948970028097, 59243719929958343565697204780596496129, 7507351981539044730893385057192143660843521
Offset: 1

Views

Author

Robert Price, Jan 30 2015

Keywords

Comments

a(12) is too large to display here. It has 46 digits and is the 158th term in A123526.

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192, A060455, A253318, A079262, A253705, A123526, A254412.

Programs

  • Mathematica
    a={1,1,1,1,1,1,1,1}; step=8; lst={}; For[n=step+1,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,sum]]; a=RotateLeft[a]; a[[step]]=sum]; lst
Select[With[{lr=PadRight[{},8,1]},LinearRecurrence[lr,lr,200]],PrimeQ] (* Harvey P. Dale, Dec 03 2022 *)

A253706 Primes in the 8th-order Fibonacci numbers A079262.

Original entry on oeis.org

2, 509, 128257, 133294824621464999938178340471931877, 4596852049500861351052672455121859744010232939954169259264638023409631672658340253083284317818242062413
Offset: 1

Views

Author

Robert Price, Jan 09 2015

Keywords

Comments

a(6) is too large to display here. It has 395 digits and is the 1322nd term in A079262.

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232543, A214899, A020992, A233554, A214727, A234696, A141523, A235862, A214825, A235873, A001630, A241660, A247027, A000288, A247561, A000322, A248920, A000383, A247192, A060455, A253318, A079262, A253705.

Programs

  • Mathematica
    a={0,0,0,0,0,0,0,1}; step=8; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,sum]]; a=RotateLeft[a]; a[[step]]=sum]; lst
  • PARI
    lista(nn) = {gf = x^7/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8); for (n=0, nn, if (isprime(p=polcoeff(gf+O(x^(n+1)), n)), print1(p, ", ")););} \\ Michel Marcus, Jan 12 2015
Showing 1-4 of 4 results.

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