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A007522 Primes of form 8n+7.
(Formerly M4376)
49
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; text; internal format)
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^2-2y^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].

FORMULA

Equals A000040 INTERSECT A004215. - R. J. Mathar, Nov 22 2006

MATHEMATICA

a={}; Do[x=8*n-1; 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, p-1, 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 !! (n-1)

a007522_list = filter ((== 1) . a010051) a004771_list

-- Reinhard Zumkeller, Jan 29 2013

CROSSREFS

Cf. A040098, A007522, A014754, A065907, A065908.

Cf. A010051, subsequence of A004771.

Sequence in context: A089199 A014663 A141175 * A157811 A227421 A098029

Adjacent sequences:  A007519 A007520 A007521 * A007523 A007524 A007525

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified April 24 04:20 EDT 2014. Contains 240947 sequences.