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Search: id:A007996
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| A007996 |
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Primes that divide at least one term of the sequence f given by f(1) = 2, f(n+1) = n^2-n+1. |
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+0
4
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| 2, 3, 7, 13, 43, 73, 139, 181, 547, 607, 1033, 1171, 1459, 1861, 1987, 2029, 2287, 2437, 4219, 4519, 6469, 7603, 8221, 9829, 12763, 13147, 13291, 13999, 15373, 17881, 17977, 19597, 20161, 20479, 20641, 20857, 20929, 21661, 23689, 23773, 27031
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Or, let S_1 = [2] and let S_{n+1} = list formed by sorting the union of S_n together with all prime factors of 1 + Product_i S_n(i) into increasing order; sequence is limit as n -> infinity of S_n.
Prime divisors of the terms of Sylverster's sequence A000058. - Max Alekseyev (maxal(AT)cs.ucsd.edu), Jan 03 2004. Also of A007018. - njas, Jan 27 2007
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REFERENCES
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R. W. K. Odoni, On the prime divisors of the sequence w_{n+1} = 1+w_1 ... w_n, J. London Math. Soc. 32 (1985), 1-11.
Filip Saidak, A New Proof of Euclid's Theorem, Amer. Math. Monthly, Dec 2006
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LINKS
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Eric Weisstein's World of Mathematics, Sylvester's sequence
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MAPLE
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n := 1; for p do if isprime(p) then x := 2 mod p; S := {}; while not member(x, S) do if x=0 then a[n] := p; n := n+1; break; fi; S := S union {x}; x := (x^2-x+1) mod p; od; fi; od;
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CROSSREFS
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The missing primes form A096264.
Cf. A000058, A014546, A091335, A091336.
Sequence in context: A078749 A046062 A096263 this_sequence A085872 A075059 A070858
Adjacent sequences: A007993 A007994 A007995 this_sequence A007997 A007998 A007999
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KEYWORD
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nonn
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AUTHOR
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Bennett Battaile (bennett.battaile(AT)autodesk.com)
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EXTENSIONS
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More terms from Max Alekseyev (maxal(AT)cs.ucsd.edu), Jan 03 2004
Entry revised by njas, Jan 28 2007
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