A381017 Prime terms of A000328.

5, 13, 29, 113, 149, 197, 317, 613, 709, 797, 1009, 1129, 1373, 3001, 3209, 3853, 4513, 5261, 6361, 7213, 11681, 12853, 15373, 16729, 19577, 20593, 21101, 22133, 25997, 30757, 33317, 38669, 53077, 56401, 65101, 68777, 72533, 73517, 95093, 100621, 108637, 114553, 115781, 118213

Offset: 1

Author

Michel Marcus, Feb 12 2025

Keywords

• nonn

Comments

Called Gauss circle primes by Ehrenborg.

Links

• Robert Israel, Table of n, a(n) for n = 1..1188
• Thomas Ehrenborg, Gauss Circle Primes, arXiv:2502.06804 [math.GM], 2025. See Table 1 p. 3.

Crossrefs

Cf. A000040, A000328, A381018.

Programs

Maple

N:= 200: # for terms in A000328(1..N)
V:= Array(0..N): V[0]:= 1:
for x from 1 to N do
  for y from 0 to x do
    if y = 0 or y = x then m:= 4 else m:= 8 fi;
    s:= ceil(sqrt(x^2+y^2));
    if s > N then break fi;
    V[s]:= V[s] + m
od od:
select(isprime, ListTools:-PartialSums(convert(V,list))); # Robert Israel, May 27 2025

PARI

select(isprime, vector(200, n, 1 + 4*sum(j=0, n^2\4, n^2\(4*j+1) - n^2\(4*j+3))))