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A293859
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Prime factors of numbers of the form k^2 + 10.
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3
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2, 5, 7, 11, 13, 19, 23, 37, 41, 47, 53, 59, 89, 103, 127, 131, 139, 157, 167, 173, 179, 197, 211, 223, 241, 251, 263, 277, 281, 293, 317, 331, 367, 373, 379, 383, 397, 401, 409, 419, 449, 463, 487, 491, 499, 503, 521, 557, 569, 571, 601, 607, 613, 619, 641
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OFFSET
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1,1
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COMMENTS
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Primes p such that Legendre(-10,p) = 0 or 1. - N. J. A. Sloane, Dec 26 2017
Question: Is there a comment of the form "a prime number is in this sequence if and only if it is congruent to (list of appropriate values) mod n" for this sequence?
Prime p > 5 is in the sequence iff -10 is a quadratic residue mod p.
Thus p is either in the intersection of A002144 and A038879 or in neither of them.
Primes == 1, 2, 5, 7, 9, 11, 13, 19, 23, or 37 (mod 40). (End)
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LINKS
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EXAMPLE
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7 is in the sequence because 2^2 + 10 = 14 is 2 times 7.
19 is in the sequence because 3^2 + 10 = 19.
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MAPLE
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select(isprime, [seq(seq(i*40+j, j = [1, 2, 5, 7, 9, 11, 13, 19, 23, 37]), i=0..40)]); # Robert Israel, Nov 19 2017
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MATHEMATICA
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Select[Prime@ Range@ 120, {} != FindInstance[# x == n^2 + 10 && n >= 0 && x > 0, {n, x}, Integers, 1] &] (* Giovanni Resta, Oct 19 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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