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A130164 Numbers k such that k^2 divides 3*Fibonacci(k). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A subset of A023172. All listed terms for n>1 are divisible by a(2) = 12 = 2^2*3. All listed terms for n>2 are divisible by a(3) = 36 = 2^2*3^2. - Robert G. Wilson v, May 15 2007
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..289 (terms < 4*10^9)
EXAMPLE
36 is a term because 36^2 = 2^4*3^4 divides 3*Fibonacci(36) = 3*14930352 = 2^4*3^4*17*19*107.
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 *)
PROG
(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", ")))
(Magma) [n: n in [1..2*10^5] | 3*Fibonacci(n) mod n^2 eq 0 ]; // Vincenzo Librandi, Sep 17 2015
CROSSREFS
Cf. A000045.
Cf. A023172 (n divides Fibonacci(n)), A130163 (n^2 divides 2*Fibonacci(n)).
Sequence in context: A085331 A225100 A058040 * A144973 A043358 A023731
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, May 14 2007
EXTENSIONS
More terms from Stefan Steinerberger and Robert G. Wilson v, May 15 2007
More terms from Robert Gerbicz, Nov 28 2010
STATUS
approved

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Last modified July 22 12:22 EDT 2024. Contains 374499 sequences. (Running on oeis4.)