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.

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

1,1

Links

Table of n, a(n) for n=1..67.

Example

5 + 8 = 13, the least Pythagorean prime after 5, and 5 + 13 - 1 = 17, a 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, A378184, A378186, A378187.

Sequence in context: A070485 A248293 A151726 * A070290 A307266 A173855

Adjacent sequences: A380556 A380557 A380558 * A380560 A380561 A380562

Keyword

nonn

Author

Clark Kimberling, Jan 26 2025

Status

approved