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Search: id:A125257
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| A125257 |
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Smallest prime divisor of 4n^2+3 that is of the form 6k+1. |
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+0
1
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| 7, 19, 13, 67, 103, 7, 199, 7, 109, 13, 487, 193, 7, 787, 7, 13, 19, 433, 1447, 7, 19, 7, 13, 769, 2503, 2707, 7, 43, 7, 1201, 3847, 4099, 1453, 7, 4903, 7, 5479, 5779, 2029, 19, 7, 13, 7, 61, 37, 8467, 8839, 7, 13, 7, 3469, 31, 11239, 3889, 7, 12547, 7, 43, 19, 4801
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Any prime divisor of 4n^2+3 different from 3 is congruent to 1 modulo 6.
4n^2+3 is never a power of 3 for n > 0; hence a prime divisor congruent to 1 modulo 6 always exists.
a(n) = 7 if and only if n is congruent to 1 or -1 modulo 7.
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REFERENCES
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D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 191.
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LINKS
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N. Hobson, Table of n, a(n) for n = 1..1000
N. Hobson, Home page (listed in lieu of email address)
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EXAMPLE
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The prime divisors of 4*3^2+3=39 are 3 and 13, so a(3) = 13.
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PROGRAM
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(PARI) vector(60, n, factor(4*n^2+3)[2-(n^2)%3, 1])
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CROSSREFS
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Cf. A057204, A124988.
Sequence in context: A024830 A030982 A070414 this_sequence A052256 A064819 A102167
Adjacent sequences: A125254 A125255 A125256 this_sequence A125258 A125259 A125260
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KEYWORD
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easy,nonn
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AUTHOR
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Nick Hobson Nov 26 2006
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