A393610 a(n) = least positive integer k such that A003627(n) + 3^k - 1 is prime, or -1 if no such prime exists.

-1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 3, 2, 1, 1, 3, 2, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 3, 3, 2, 1, 1, 4, 1, 4, 1, 3, 2, 3, 2, 2, 1, 1, 4, 2, 1, 4, 2, 2, 6, 5, 1, 12, 2, 1, 3, 2, 1, 1, 1, 3, 2, 1, 4, 2, 2, 2, 2, 2, 4, 3, 1, 1, 1, 4, 1, 7, 1, 4, 2, 2, 3, 8, 4, 3, 7, 2

Offset

1,5

Links

Table of n, a(n) for n=1..87.

Example

A003626(8) = 47; 47 + 3*1 - 1 = 49 (not prime), 47 + 3^2 - 1 = 56 (not prime), 47 + 3^3 - 1 = 73, a prime, so a(8) = 3.

Mathematica

s = Select[Prime[Range[400]], Mod[#, 3] == 2 &]; (* A003627 *)
g[n_] := s[[n]];
f[n_] := Select[Range[200], PrimeQ[g[n] + 3^# - 1] &, 1];
Join[{-1}, Flatten[Table[f[n], {n, 2, 200}]]]

Crossrefs

Cf. A000040, A003627, A094076, A393611.

Sequence in context: A184441 A172279 A348285 * A164953 A136622 A025474

Adjacent sequences: A393607 A393608 A393609 * A393611 A393612 A393613

Keyword

sign

Author

Clark Kimberling, Feb 24 2026

Status

approved