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Search: id:A125256
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| A125256 |
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Smallest odd prime divisor of n^2+1. |
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+0
1
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| 5, 5, 17, 13, 37, 5, 5, 41, 101, 61, 5, 5, 197, 113, 257, 5, 5, 181, 401, 13, 5, 5, 577, 313, 677, 5, 5, 421, 17, 13, 5, 5, 13, 613, 1297, 5, 5, 761, 1601, 29, 5, 5, 13, 1013, 29, 5, 5, 1201, 41, 1301, 5, 5, 2917, 17, 3137, 5, 5, 1741, 13, 1861, 5, 5, 17, 2113, 4357, 5, 5
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Any odd prime divisor of n^2+1 is congruent to 1 modulo 4.
n^2+1 is never a power of 2 for n > 1; hence a prime divisor congruent to 1 modulo 4 always exists.
a(n) = 5 if and only if n is congruent to 2 or -2 modulo 5.
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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 = 2..1000
N. Hobson, Home page (listed in lieu of email address)
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EXAMPLE
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The prime divisors of 8^2+1=65 are 5 and 13, so a(7) = 5.
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PROGRAM
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(PARI) vector(68, n, if(n<2, "-", factor(n^2+1)[1+(n%2), 1]))
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CROSSREFS
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Cf. A002522, A002496, A014442, A057207.
Adjacent sequences: A125253 A125254 A125255 this_sequence A125257 A125258 A125259
Sequence in context: A140360 A072272 A079317 this_sequence A075684 A095342 A100745
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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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