A378184 With p(n) = A002144(n) = n-th Pythagorean prime, a(n) is the least k such p(n) + k is a Pythagorean prime and 2 p(n) + k + 1 is a non-Pythagorean prime; or a(n) = 0 if there is no such k.

8, 4, 12, 8, 4, 20, 20, 28, 16, 12, 4, 8, 4, 24, 36, 8, 16, 20, 16, 76, 36, 4, 24, 16, 56, 8, 16, 36, 20, 4, 56, 16, 40, 20, 76, 8, 64, 8, 40, 40, 16, 8, 4, 48, 12, 20, 36, 24, 16, 116, 76, 4, 24, 20, 20, 100, 100, 84, 56, 52, 64, 16, 8, 4, 24, 12, 44, 56

Offset

1,1

Links

Table of n, a(n) for n=1..68.

Example

5 + 8 = 13, the least Pythagorean prime after 5, and 5 + 13 + 1 = 19, a non-Pythagorean prime, so a(1) = 8.

Mathematica

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

Crossrefs

Cf., A000041, A002144, A002145.

Sequence in context: A194217 A239971 A082073 * A244209 A156279 A203072

Adjacent sequences: A378181 A378182 A378183 * A378185 A378186 A378187

Keyword

nonn

Author

Clark Kimberling, Jan 11 2025

Status

approved