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Search: id:A000057
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| A000057 |
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Primes dividing all Fibonacci sequences.
(Formerly M0856 N0326)
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+0
6
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| 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)
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OFFSET
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1,1
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COMMENT
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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
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REFERENCES
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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).
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LINKS
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Christian G. Bower, Table of n, a(n) for n = 1..160
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Don Reble (djr(AT)nk.ca), Nov 14 2006
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