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A219612
Numbers k that divide the sum of the first k Fibonacci numbers (beginning with F(0)).
4
1, 4, 6, 9, 11, 19, 24, 29, 31, 34, 41, 46, 48, 59, 61, 71, 72, 79, 89, 94, 96, 100, 101, 106, 109, 120, 129, 131, 139, 144, 149, 151, 166, 179, 181, 191, 192, 199, 201, 211, 214, 216, 220, 226, 229, 239, 240, 241, 249, 251, 269, 271, 274, 281, 288, 311
OFFSET
1,2
COMMENTS
Numbers k such that A000045(k+1) == 1 (mod k). - Robert Israel, Oct 13 2015
LINKS
FORMULA
a(n) = A101907(n) + 1. - Altug Alkan, Dec 29 2015
EXAMPLE
Sum of first 6 Fibonacci numbers is 0+1+1+2+3+5 = 12. Because 6 divides 12, 6 is in the sequence.
MAPLE
fmod:= proc(a, b) local A, n, f1, f2, f;
uses LinearAlgebra[Modular];
A:= Mod(b, <<1, 1>|<1, 0>>, integer[8]);
MatrixPower(b, M, a)[1, 2];
end proc:
1, op(select(t -> fmod(t+1, t) = 1, [$2..10^4])); # Robert Israel, Oct 13 2015
MATHEMATICA
okQ[n_] := n == 1 || Mod[Fibonacci[n+1], n] == 1;
Select[Range[1000], okQ] (* Jean-François Alcover, Feb 04 2023 *)
PROG
(Python)
sum, prpr, prev = 0, 0, 1
for i in range(1, 1000):
sum += prpr
if sum % i == 0: print i,
prpr, prev = prev, prpr+prev
(PARI) lista(nn) = {sf = 0; for (n=0, nn, sf += fibonacci(n); if (sf % (n+1) == 0, print1(n+1, ", ")); ); } \\ Michel Marcus, Jun 05 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, May 03 2013
STATUS
approved