A130163 Numbers k such that k^2 divides 2*Fibonacci(k).
1, 12, 24, 168, 552, 2184, 3864, 4872, 13944, 28056, 35448, 47208, 50232, 63336, 70728, 75624, 76728, 112056, 172536, 181272, 224952, 239736, 254472, 287448, 320712, 364728, 381432, 404376, 457608, 460824, 508872, 529368, 537096, 613704, 645288, 813624
Offset: 1
Keywords
Examples
24 is a term because 24^2 = 2^6*3^2 divides 2*Fibonacci(24) = 2*46368 = 2^6*3^2*7*23.
Links
- Keith Schneider and Giovanni Resta, Table of n, a(n) for n = 1..776 (terms < 4*10^9, first 39 terms from Keith Schneider)
Programs
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Magma
[n: n in [1..2*10^5] | 2*Fibonacci(n) mod n^2 eq 0 ]; // Vincenzo Librandi, Sep 17 2015
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Mathematica
a=0; b=1; c=1; Do[a=b; b=c; c=a+b; If[Mod[2c,(n+2)^2]==0,Print[n+2]],{n,1,40000}] (* Stefan Steinerberger, May 15 2007 *) A130163 = {1}; a = 0; b = 12; c = 3864; Do[If[Mod[24b, n^2] == 0, A130163 = Append[A130163, n]]; a = b; b = c; c = 322b - a;, {n, 12, 1000000, 12}]; A130163 Length[A130163] (* Keith Schneider, May 27 2007 *)
Extensions
More terms from Stefan Steinerberger, May 15 2007
a(14) corrected by N. J. A. Sloane, Nov 23 2007
Comments