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A038873
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Primes p such that 2 is a square mod p; or, primes congruent to {1, 2, 7} mod 8.
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18
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2, 7, 17, 23, 31, 41, 47, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 311, 313, 337, 353, 359, 367, 383, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593, 599, 601, 607, 617
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OFFSET
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1,1
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COMMENTS
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Same as A001132 except for initial term.
Primes p such that x^2 = 2 has a solution mod p.
The prime values of the form x^2 + 2xy - y^2 coincide with this sequence. These are also primes of the form u^2 - 2v^2. - Tito Piezas III, Dec 28 2008
Therefore these are composite in Z[sqrt(2)], as they can be factored as (u^2 - 2v^2)(u^2 + 2v^2). - Alonso del Arte, Oct 03 2012
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 1..10000
K. S. Brown, Pythagorean graphs
Index entries for related sequences
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MAPLE
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seq(`if`(member(ithprime(n) mod 8, {1, 2, 7}), ithprime(n), NULL), n=1..113); # Nathaniel Johnston, Jun 26 2011
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MATHEMATICA
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fQ[n_] := MemberQ[{1, 2, 7}, Mod[n, 8]]; Select[ Prime[Range[114]], fQ] (* Robert G. Wilson v, Oct 18 2011 *)
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PROG
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(MAGMA) [ p: p in PrimesUpTo(617) | IsSquare(R!2) where R:=ResidueClassRing(p) ]; // From Klaus Brockhaus, Dec 02 2008
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CROSSREFS
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Cf. A057126, A087780.
Sequence in context: A074884 A105911 * A141131 A049594 A049590 A049570
Adjacent sequences: A038870 A038871 A038872 * A038874 A038875 A038876
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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