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A118917 Number of inequivalent primes in ring of integers Z[sqrt(2)] with absolute value of norm = n. 3
0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Since there are infinitely many units in Z[sqrt(2)], the total number of primes with a given norm is infinite (when there are any).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

FORMULA

a(n) = 2 if n is a prime = 1,7 (mod 8); a(n) = 1 if n is 2 or p^2 where p is a prime = 3,5 (mod 8); otherwise a(n) = 0.

MATHEMATICA

a[n_] := Which[PrimeQ[n] && MatchQ[Mod[n, 8], 1|7], 2, p = Sqrt[n]; n == 2 || IntegerQ[p] && PrimeQ[p] && MatchQ[Mod[p, 8], 3|5], 1, True, 0]; Table[a[n], {n, 0, 104}] (* Jean-Fran├žois Alcover, Nov 22 2016 *)

PROG

(PARI) A118917(n) = { my(p); if(isprime(n)&&((1==(n%8))||(7==(n%8))), 2, if((2==n)||((issquare(n, &p)&&isprime(p))&&((3==(p%8))||(5==(p%8)))), 1, 0)); }; \\ Antti Karttunen, Aug 30 2017

CROSSREFS

Cf. A055029, A118916.

Sequence in context: A258822 A064530 A037047 * A325045 A204293 A206479

Adjacent sequences:  A118914 A118915 A118916 * A118918 A118919 A118920

KEYWORD

easy,nice,nonn

AUTHOR

Franklin T. Adams-Watters, May 05 2006

STATUS

approved

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Last modified April 20 08:50 EDT 2019. Contains 322306 sequences. (Running on oeis4.)