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Search: id:A005529
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| A005529 |
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Primitive prime factors of the sequence k^2 + 1 (A002522) in the order that they are found.
(Formerly M1505)
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+0
4
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| 2, 5, 17, 13, 37, 41, 101, 61, 29, 197, 113, 257, 181, 401, 97, 53, 577, 313, 677, 73, 157, 421, 109, 89, 613, 1297, 137, 761, 1601, 353, 149, 1013, 461, 1201, 1301, 541, 281, 2917, 3137, 673, 1741, 277, 1861, 769, 397, 241, 2113, 4357, 449, 2381, 2521, 5477
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes associated with Stormer numbers.
See A002313 for the sorted list of primes. It can be shown that k^2 + 1 has at most one primitive prime factor; the other prime factors divide m^2 + 1 for some m < k. When k^2 + 1 has a primitive prime factor, k is a Stormer number (A005528), otherwise a non-Stormer number (A002312).
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REFERENCES
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John H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, p. 246.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Todd, Table of Arctangents. National Bureau of Standards, Washington, DC, 1951, p. vi.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Primitive Prime Factor
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MATHEMATICA
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prms={}; Do[f=First/@FactorInteger[k^2+1]; p=Complement[f, prms]; prms=Join[prms, p], {k, 100}]; prms
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PROGRAM
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(MAGMA) V:=[]; for n in [1..75] do p:=Max([ x[1]: x in Factorization(n^2+1) ]); if not p in V then Append(~V, p); end if; end for; V; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 29 2008]
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CROSSREFS
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Cf. A002312, A002313 (primes of the form 4k+1), A002522, A005528.
Sequence in context: A037075 A115894 A033835 this_sequence A057282 A123364 A025553
Adjacent sequences: A005526 A005527 A005528 this_sequence A005530 A005531 A005532
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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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Edited by T. D. Noe (noe(AT)sspectra.com), Oct 02 2003
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