cp's OEIS Frontend

A381017 Prime terms of A000328.

%I A381017 #13 May 28 2025 16:25:54
%S A381017 5,13,29,113,149,197,317,613,709,797,1009,1129,1373,3001,3209,3853,
%T A381017 4513,5261,6361,7213,11681,12853,15373,16729,19577,20593,21101,22133,
%U A381017 25997,30757,33317,38669,53077,56401,65101,68777,72533,73517,95093,100621,108637,114553,115781,118213
%N A381017 Prime terms of A000328.
%C A381017 Called Gauss circle primes by Ehrenborg.
%H A381017 Robert Israel, <a href="/A381017/b381017.txt">Table of n, a(n) for n = 1..1188</a>
%H A381017 Thomas Ehrenborg, <a href="https://arxiv.org/abs/2502.06804">Gauss Circle Primes</a>, arXiv:2502.06804 [math.GM], 2025. See Table 1 p. 3.
%p A381017 N:= 200: # for terms in A000328(1..N)
%p A381017 V:= Array(0..N): V[0]:= 1:
%p A381017 for x from 1 to N do
%p A381017   for y from 0 to x do
%p A381017     if y = 0 or y = x then m:= 4 else m:= 8 fi;
%p A381017     s:= ceil(sqrt(x^2+y^2));
%p A381017     if s > N then break fi;
%p A381017     V[s]:= V[s] + m
%p A381017 od od:
%p A381017 select(isprime, ListTools:-PartialSums(convert(V,list))); # _Robert Israel_, May 27 2025
%o A381017 (PARI) select(isprime, vector(200, n, 1 + 4*sum(j=0, n^2\4, n^2\(4*j+1) - n^2\(4*j+3))))
%Y A381017 Cf. A000040, A000328, A381018.
%K A381017 nonn
%O A381017 1,1
%A A381017 _Michel Marcus_, Feb 12 2025