|
Search: id:A000057
|
|
|
| A000057 |
|
Primes dividing all Fibonacci sequences.
(Formerly M0856 N0326)
|
|
+0
6
|
|
| 2, 3, 7, 23, 43, 67, 83, 103, 127, 163, 167, 223, 227, 283, 367, 383, 443, 463, 467, 487, 503, 523, 547, 587, 607, 643, 647, 683, 727, 787, 823, 827, 863, 883, 887, 907, 947, 983, 1063, 1123, 1163, 1187, 1283, 1303, 1327, 1367, 1423, 1447, 1487, 1543
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Here a Fibonacci sequence is a sequence which begins with any two integers and continues using the rule s(n+2) = s(n+1) + s(n). These primes divide at least one number in each such sequence. - Don Reble, Dec 15 2006
Primes p such that the smallest positive n for which Fibonacci(n) = 0 mod p is n=p+1. In other words, the nth prime p is in this sequence iff A001602(n)=p+1. - Max Alekseyev (maxale(AT)gmail.com), Nov 23 2007
|
|
REFERENCES
|
U. Alfred, Primes which are factors of all Fibonacci sequences, Fib. Quart., 2 (1964), 33-38.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
Christian G. Bower, Table of n, a(n) for n = 1..160
|
|
CROSSREFS
|
Subset of A064414.
Cf. A106535, A079346.
Sequence in context: A072686 A002230 A106865 this_sequence A037231 A082449 A129741
Adjacent sequences: A000054 A000055 A000056 this_sequence A000058 A000059 A000060
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from Don Reble (djr(AT)nk.ca), Nov 14 2006
|
|
|
Search completed in 0.002 seconds
|
