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A187966
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Numbers n for which Fibonacci(n) mod n equals some nonzero Fibonacci(k) and k divides n.
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1
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2, 3, 4, 6, 10, 11, 14, 19, 20, 22, 29, 31, 38, 41, 54, 55, 56, 58, 59, 61, 62, 71, 76, 79, 80, 82, 89, 93, 95, 101, 109, 110, 118, 121, 122, 123, 124, 131, 139, 142, 145, 149, 151, 152, 153, 155, 158, 165, 174, 178, 179, 181, 190, 191, 196, 199, 202, 205, 209, 211, 213
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OFFSET
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1,1
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COMMENTS
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If Fibonacci(n) (mod n) = 1, then we assume that k=1 (even though Fibonacci(2) also equals 1). Subsequence of A182625.
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 1..2000
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EXAMPLE
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14 is in this sequence because fib(14)=377 is congruent to 13 (mod 14), 13=fib(7), and 7 divides 14.
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MATHEMATICA
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nn = 13; f = Table[Fibonacci[n], {n, nn}]; okQ[n_] := Module[{pos = Position[f, Mod[Fibonacci[n], n]]}, pos != {} && Mod[n, pos[[1, 1]]] == 0]; Select[Range[f[[-1]]], okQ] (* T. D. Noe, Apr 04 2011 *)
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PROG
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(PARI) ok(n)={my(m=fibonacci(n)%n); fordiv(n, k, my(t=fibonacci(k)); if(t>=m, return(t==m))); 0} \\ Andrew Howroyd, Feb 25 2018
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CROSSREFS
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Cf. A182625.
Sequence in context: A005457 A005453 A180242 * A280584 A225649 A225651
Adjacent sequences: A187963 A187964 A187965 * A187967 A187968 A187969
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KEYWORD
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nonn
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AUTHOR
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Carmine Suriano, Mar 30 2011
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STATUS
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approved
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