A284376 a(n) is the least nonnegative integer such that n + i*a(n) is a Gaussian prime.

3, 1, 1, 0, 1, 2, 1, 0, 3, 4, 1, 0, 7, 2, 1, 2, 1, 2, 5, 0, 1, 4, 5, 0, 1, 4, 1, 2, 5, 4, 11, 0, 3, 2, 5, 2, 1, 2, 3, 10, 1, 4, 5, 0, 9, 2, 5, 0, 13, 4, 7, 4, 3, 10, 1, 4, 1, 2, 3, 0, 13, 10, 3, 32, 9, 2, 1, 0, 5, 10, 3, 0, 5, 2, 1, 4, 5, 10, 7, 0, 7, 4, 3, 0, 1, 2, 9, 2, 3, 4, 1, 4, 7, 8, 1, 2, 5, 2, 3, 4, 3

Offset

0,1

Links

Lars-Erik Svahn, Table of n, a(n) for n = 0..10000

Lars-Erik Svahn, numbertheory.4th

Akshaa Vatwani, Bounded gaps between Gaussian primes, Journal of Number Theory, Volume 171, February 2017, Pages 449-473.

Wikipedia, Gaussian prime

Index entries for Gaussian integers and primes

Formula

From Michel Marcus, Mar 30 2017: (Start)

a(n) = 0 for n in A002145.

a(n) = 1 for n in A005574.

(End)

a(n) = A069003(n) if n is not in A002145. - Robert Israel, Apr 07 2017

Maple

f:= proc(n) local k;
  for k from 0 do if GaussInt:-GIprime(n+I*k) then return k fi od
end proc:
map(f, [$0..100]); # Robert Israel, Apr 07 2017

Mathematica

Table[k = 0; While[! PrimeQ[n + I k, GaussianIntegers -> True], k++]; k, {n, 0, 100}] (* Michael De Vlieger, Mar 29 2017 *)

Prog

(ANS-Forth)
s" numbertheory.4th" included
: 3mod4_prime \ n -- flag
  abs dup isprime swap 3 and 3 = and ;
: isGaussianPrime \ a b -- flag
  over 0= if nip 3mod4_prime exit then
  dup 0= if drop 3mod4_prime exit then
  dup * swap dup * + isprime ;
: Gauss_prime \ n -- a(n)
  0
  begin 2dup isGaussianPrime 0=
  while 1+
  repeat nip ;

Crossrefs

Cf. A002145, A005574, A069003.

Sequence in context: A338638 A062172 A196838 * A088205 A318923 A336111

Adjacent sequences: A284373 A284374 A284375 * A284377 A284378 A284379

Keyword

nonn

Author

Lars-Erik Svahn, Mar 25 2017

Status

approved