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 1-3 of 3 results.

A159259 Positive numbers n such that 8*n^2-2*n-1 divides Fibonacci(n).

Original entry on oeis.org

27, 37, 97, 577, 687, 727, 777, 807, 1297, 1707, 1917, 2067, 2487, 2787, 2977, 3027, 3037, 3067, 3277, 3367, 3417, 3507, 3837, 4047, 4257, 4377, 4447, 4567, 4717, 5137, 5557, 5637, 5677, 5917, 5967, 6057, 6187, 6327, 7077, 7087, 7357, 7407, 7507, 7597
Offset: 1

Views

Author

Arkadiusz Wesolowski, Apr 07 2009

Keywords

Comments

The prime numbers of this sequence are in A159231.

Links

Crossrefs

Cf. A000045, A023172, A159234, A159231, A181890.

Programs

  • Magma
    [n : n in [1..7597] | IsZero(Fibonacci(n) mod (8*n^2-2*n-1))] // Arkadiusz Wesolowski, Nov 09 2013
  • Mathematica
    Select[Range[7597], Mod[Fibonacci[#], 8*#^2 - 2*# - 1] == 0 &] (* Arkadiusz Wesolowski, Dec 12 2011 *)
  • PARI
    for(n=1, 7597, if(Mod(fibonacci(n), 8*n^2-2*n-1)==0, print1(n, ", "))); \\ Arkadiusz Wesolowski, Nov 09 2013

A159234 Composite numbers n such that 8*n^2-2*n-1 divides the primitive part U(n) of Fibonacci(n).

Original entry on oeis.org

27, 807, 1707, 2977, 3027, 3277, 4717, 5137, 5677, 5917, 5967, 6187, 7087, 7357, 7597, 7707, 8217, 9117, 9297, 9387, 9667, 9877, 9927, 9997, 10387, 11097, 11647, 11797, 12727, 13407, 13867, 15757, 15987, 16327, 16507, 16857, 17347, 17767, 18237, 18817, 18997
Offset: 1

Views

Author

Arkadiusz Wesolowski, Apr 06 2009

Keywords

Links

Crossrefs

Subsequence of A159259.
Cf. A000045, A023172, A061446, A159231, A181890.

Programs

  • Mathematica
    lst = {1}; Do[f = Fibonacci[a]; Do[f = f/GCD[f, lst[[d]]], {d, Most[Divisors[a]]}]; AppendTo[lst, f], {a, 2, 19000}]; Flatten[Table[If[! PrimeQ[n] && Mod[lst[[n]], 8*n^2 - 2*n - 1] == 0, n, {}], {n, 19000}]] (* Arkadiusz Wesolowski, Dec 12 2011 *)

A215158 Primes p such that (2*p - 1)*(4*p + 1)*(14*p - 1) divides Fibonacci(p).

Original entry on oeis.org

727, 7507, 58417, 164767, 192697, 260317, 362977, 624847, 800557, 838837, 946417, 2107447, 2334187, 2382607, 2461717, 2495947, 2523517, 2566027, 2923747, 3169237, 3373177, 3373687, 3763717, 3771907, 3838897, 4143637, 4635277, 4741837, 4979047, 5097247
Offset: 1

Views

Author

Arkadiusz Wesolowski, Aug 04 2012

Keywords

Links

Crossrefs

Subsequence of A159231.
Cf. A000045, A159259.

Programs

  • Mathematica
    Select[Prime@Range[10^3], Mod[Fibonacci[#], 112*#^3 - 36*#^2 - 12*# + 1] == 0 &]
  • PARI
    a=-1; b=1; for(n=0, 2548623, a=a+b; b=b+a; p=2*n+1; if(isprime(p)&&Mod(b, 112*p^3-36*p^2-12*p+1)==0, print1(p, ", "))); \\ Arkadiusz Wesolowski, Nov 16 2013
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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