A393613 a(n) = least positive integer k such that prime(n) + 2^k + 4 is prime, or -1 if no such prime exists.

-1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 5, 1, 1, 2, 1, 1, 2, 1, 7, 1, 2, 1, 1, 1, 1, 7, 5, 3, 1, 3, 3, 2, 1, 1, 5, 1, 1, 3, 3, 1, 1, 5, 3, 3, 1, 1, 3, 1, 3, 5, 1, 1, 1, 2, 1, 1, 3, 29, 4, 1, 1, 5, 4, 1, 3, 1, 27, 1, 2, 1, 1, 15, 1, 2, 3, 2, 3, 3, 3, 2, 1, 7

Offset

1,2

Links

Table of n, a(n) for n=1..85.

Example

3 + 2^1 + 4 = 9 (not prime); 3 + 2^2 + 4 = 11 (prime), so a(2) = 2.

Mathematica

f[n_] := Select[Range[100], PrimeQ[Prime[n] + 2^# + 4] &, 1];
Join[{-1}, Flatten[Table[f[n], {n, 1, 120}]]]

Crossrefs

Cf. A000040, A094076, A393612.

Sequence in context: A062760 A323163 A322318 * A014649 A326568 A279817

Adjacent sequences: A393610 A393611 A393612 * A393614 A393615 A393616

Keyword

sign

Author

Clark Kimberling, Mar 01 2026

Status

approved