

A007522


Primes of the form 8n+7, that is, primes congruent to 1 mod 8.
(Formerly M4376)


64



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
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OFFSET

1,1


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, Nov 28 2001
Is this the same sequence as A141175?
As this is a subset of A001132, this is also a subset of the primes of form x^22y^2.  Tito Piezas III, Dec 28 2008
Primes that are the sum of no fewer than four positive squares.
Subsequence of A141164.  Reinhard Zumkeller, Mar 26 2011
Also a subsequence of primes of the form x^2 + y^2 + z^2 + 1.  Arkadiusz Wesolowski, Apr 05 2012
Primes p such that p XOR 6 = p  6.  Brad Clardy, Jul 22 2012


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).


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].N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)


FORMULA

Equals A000040 INTERSECT A004215.  R. J. Mathar, Nov 22 2006
a(n) = 7 + A139487(n)*8, n >= 1.  Wolfdieter Lang, Feb 18 2015


MATHEMATICA

a={}; Do[x=8*n1; If[PrimeQ[x], AppendTo[a, x]], {n, 10^2}]; a  Vladimir Joseph Stephan Orlovsky, Apr 29 2008


PROG

(PARI) A007522(m) = local(p, s, x, z); forprime(p = 3, m, s = []; for(x = 0, p1, if(x^4%p == 2%p, s = concat(s, [x]))); z = matsize(s)[2]; if(z == 2, print1(p, ", "))) A007522(1400)
(Haskell)
a007522 n = a007522_list !! (n1)
a007522_list = filter ((== 1) . a010051) a004771_list
 Reinhard Zumkeller, Jan 29 2013
(MAGMA) [p: p in PrimesUpTo(2000)  p mod 8 eq 7]; // Vincenzo Librandi, Jun 26 2014


CROSSREFS

Subsequence of A004771.
Cf. A040098, A014754, A065907, A065908, A010051.
Sequence in context: A089199 A263874 A014663 * A141175 A157811 A227421
Adjacent sequences: A007519 A007520 A007521 * A007523 A007524 A007525


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Robert G. Wilson v


STATUS

approved



