|
|
A069106
|
|
Composite numbers k such that k divides F(k-1) where F(j) are the Fibonacci numbers.
|
|
11
|
|
|
442, 1891, 2737, 4181, 6601, 6721, 8149, 13201, 13981, 15251, 17119, 17711, 30889, 34561, 40501, 51841, 52701, 64079, 64681, 67861, 68101, 68251, 78409, 88601, 88831, 90061, 96049, 97921, 115231, 118441, 138601, 145351, 146611, 150121, 153781, 163081, 179697, 186961, 191351, 194833
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Primes p congruent to 1 or 4 (mod 5) divide F(p-1) (cf. A045468 and [Hardy and Wright].
|
|
REFERENCES
|
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers (Fifth edition), Oxford Univ. Press (Clarendon), 1979, Chap. X, p. 150.
|
|
LINKS
|
|
|
MATHEMATICA
|
A069106[nn_] := Select[Complement[Range[2, nn], Prime[Range[2, PrimePi[ nn]]]], Divisible[ Fibonacci[ #-1], #]&] (* Harvey P. Dale, Jul 05 2011 *)
|
|
PROG
|
(C) #include <stdio.h> #include <gmp.h> #define STARTN 10 #define N_OF_MILLER_RABIN_TESTS 5 int main() { mpz_t n, f1, f2; int flag=0; /* flag? 0: f1 contains current F[n-1] 1: f2 = F[n-1] */ mpz_set_ui (n, STARTN); mpz_init (f1); mpz_init (f2); mpz_fib2_ui (f1, f2, STARTN-1); for (;; ) { if (mpz_probab_prime_p (n, N_OF_MILLER_RABIN_TESTS)) goto next_iter; if (mpz_divisible_p (!flag? f1:f2, n)) { mpz_out_str (stdout, 10, n); printf (" "); fflush (stdout); } next_iter: mpz_add_ui (n, n, 1); mpz_add (!flag? f2:f1, f1, f2); flag = !flag; } }
(Haskell)
a069106 n = a069106_list !! (n-1)
a069106_list = [x | x <- a002808_list, a000045 (x-1) `mod` x == 0]
(PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nice,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Corrected and extended (with C program) by Ralf Stephan, Oct 13 2002
|
|
STATUS
|
approved
|
|
|
|