|
Search: id:A069106
|
|
|
| A069106 |
|
Composite n such that n divides F(n-1) where F(k) are the Fibonacci numbers. |
|
+0
8
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Primes p congruent to 1 or 4 (mod 5) divide F(p-1) (cf. A045468 and Hardy and Wright, An introduction to number theory, Chap.X, p. 150, Oxford University Press,Fifth edition).
|
|
PROGRAM
|
(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; } }
|
|
CROSSREFS
|
Cf. A045468, A003631, A064739, A081264 (Fibonacci pseudoprimes).
Sequence in context: A075268 A031609 A031720 this_sequence A094410 A105922 A018237
Adjacent sequences: A069103 A069104 A069105 this_sequence A069107 A069108 A069109
|
|
KEYWORD
|
easy,nice,nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 06 2002
|
|
EXTENSIONS
|
Corrected and extended (with C program) by Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 13 2002
|
|
|
Search completed in 0.002 seconds
|
