|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
|
|
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;
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|