A378186 -id:A378186 - cp's OEIS frontend

A378187 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 - 3 is a Pythagorean prime; and a(n) = 0 if there is no such k.

4, 12, 12, 12, 24, 12, 24, 12, 12, 36, 12, 24, 48, 24, 60, 12, 48, 72, 12, 36, 192, 12, 60, 24, 12, 48, 12, 12, 108, 48, 60, 24, 72, 72, 168, 36, 24, 12, 84, 48, 24, 48, 108, 24, 24, 36, 12, 12, 12, 24, 60, 48, 60, 156, 48, 60, 84, 12, 24, 60, 84, 12, 84, 36

Offset: 1

Clark Kimberling, Jan 13 2025

nonn

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

Cf. A000041, A002144, A002145, A378186.

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

A380559 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 Pythagorean prime; set a(n) = 0 if there is no such k.

Original entry on oeis.org

8, 4, 20, 32, 16, 20, 8, 28, 28, 20, 4, 56, 40, 44, 20, 92, 24, 8, 12, 4, 116, 4, 44, 28, 56, 80, 4, 32, 56, 36, 20, 36, 4, 56, 16, 20, 4, 8, 12, 12, 16, 152, 64, 140, 32, 20, 16, 104, 44, 40, 8, 12, 4, 44, 20, 56, 40, 28, 56, 8, 64, 24, 40, 92, 60, 56, 140

Offset: 1

Clark Kimberling, Jan 26 2025

nonn

			5 + 8 = 13, the least Pythagorean prime after 5, and 5 + 13 - 1 = 17, a Pythagorean prime, so a(1) = 8.

Cf. A000041, A002144, A002145, A378184, A378186, A378187.

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}]]

cp's OEIS Frontend

A378187 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 - 3 is a Pythagorean prime; and a(n) = 0 if there is no such k.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica