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

Author

Lars-Erik Svahn, Mar 25 2017

Keywords

• nonn

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

Crossrefs

Cf. A002145, A005574, A069003.

Programs

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 *)

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