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A007522
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Primes of form 8n+7.
(Formerly M4376)
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47
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7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 887, 911, 919, 967, 983, 991, 1031, 1039, 1063, 1087, 1103, 1151
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Primes p such that x^4 = 2 has just two solutions mod p. Subsequence of A040098. Solutions mod p are represented by integers from 0 to p - 1. For p > 2, i is a solution mod p of x^4 = 2 iff p - i is a solution mod p of x^4 = 2, so the sum of the two solutions is p. The solutions are given in A065907 and A065908. - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 28 2001
Is this the same sequence as A141175?
Contribution from Tito Piezas III (tpiezas(AT)gmail.com), Dec 28 2008: (Start)
As this is a subset of A001132, this is also a subset of the primes of form x^2-2y^2.
(End)
Primes that are the sum of no fewer than four positive squares.
Subsequence of A141164. - Reinhard Zumkeller, Mar 26 2011
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REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
| Equals A000040 INTERSECT A004215. R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 22 2006
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MATHEMATICA
| a={}; Do[x=8*n-1; If[PrimeQ[x], AppendTo[a, x]], {n, 10^2}]; a - Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 29 2008
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PROG
| (PARI): A007522(m) = local(p, s, x, z); forprime(p = 3, m, s = []; for(x = 0, p-1, if(x^4%p == 2%p, s = concat(s, [x]))); z = matsize(s)[2]; if(z == 2, print1(p, ", "))) A007522(1400)
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CROSSREFS
| Cf. A040098, A007522, A014754, A065907, A065908.
Sequence in context: A089199 A014663 A141175 * A157811 A098029 A098039
Adjacent sequences: A007519 A007520 A007521 * A007523 A007524 A007525
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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