A378186 With p(n) = A002145(n) = n-th non-Pythagorean prime, a(n) is the least k such p(n) + k is a non-Pythagorean prime and 2 p(n) + k - 5 is a Pythagorean prime; and a(n) = 0 if there is no such k .

4, 4, 12, 4, 20, 16, 16, 12, 24, 64, 12, 4, 20, 28, 20, 64, 20, 40, 16, 16, 24, 20, 20, 28, 16, 16, 12, 68, 12, 20, 40, 100, 4, 36, 16, 12, 20, 100, 4, 36, 20, 72, 4, 48, 16, 12, 24, 100, 32, 4, 20, 76, 40, 8, 16, 12, 8, 40, 64, 196, 16, 12, 60, 68, 52, 20

Offset: 1

Author

Clark Kimberling, Jan 13 2025

Keywords

• nonn

Examples

			3 + 4 = 7, the least non-Pythagorean prime after 3,
and 3 + 7 - 5 = 5, a Pythagorean prime, so a(1) = 4.
		

Crossrefs

Cf. A000041, A002144, A002145, A378187.

Programs

Mathematica

s = Select[Prime[Range[450]], Mod[#, 4] == 3 &]
a[n_] := Select[Range[200],  MemberQ[s, s[[n]] + #] && PrimeQ[2 s[[n]] + # - 5] &, 1]
Flatten[Table[a[n], {n, 1, 140}]]