A130164 Numbers k such that k^2 divides 3*Fibonacci(k).
1, 12, 36, 612, 684, 3852, 11628, 25308, 41004, 65484, 73188, 77292, 155268, 156636, 250308, 430236, 467172, 545148, 562428, 779076, 977364, 1244196, 1313964, 1847484, 2123028, 2185452, 2621196, 2639556, 2662812, 2707956, 2859804, 3770892, 4387428, 4679244, 4755852, 4942116, 5744916, 5795532, 6394716, 7941924, 8053308, 8270244, 9267516
Offset: 1
Keywords
Examples
36 is a term because 36^2 = 2^4*3^4 divides 3*Fibonacci(36) = 3*14930352 = 2^4*3^4*17*19*107.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..289 (terms < 4*10^9)
Programs
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Magma
[n: n in [1..2*10^5] | 3*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[3c,(n+2)^2 ] == 0, Print[n+2]],{n, 1, 30000}] (* Stefan Steinerberger, May 15 2007 *) a = 0; b = 0; c = 1; lst = {}; Do[ If[ Mod[3c, n^2] == 0, AppendTo[lst, n]]; a = b; b = c; c = a + b; {n, 2000000}]; lst (* Robert G. Wilson v *) A130164 = {1}; a = 0; b = 12; c = 3864; Do[If[Mod[36b, n^2] == 0, A130164 = Append[A130164, n]]; a = b; b = c; c = 322b - a;, {n, 12, 1000000, 12}]; A130164 Length[A130164] (* Keith Schneider, May 27 2007 *) -
PARI
for(n=1,10^7,A=matrix(2,2,i,j,Mod(1,n*n)*(i+j<4))^n;if(lift(3*A[1,2])==0,print1(n",")))
Extensions
More terms from Stefan Steinerberger and Robert G. Wilson v, May 15 2007
More terms from Robert Gerbicz, Nov 28 2010
Comments