A393709 a(n) = least positive integer k such that (prime(n) + 3^k)/2 is prime, or -1 if no such prime exists.

-1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 4, 1, 3, 2, 1, 4, 3, 1, 2, 1, 1, 6, 2, 8, 1, 3, 2, 2, 71, 1, 2, 1, 2, 3, 2, 1, 3, 4, 3, 4, 1, 2, 2, 1, 1, 1, 3, 6, 4, 5, 12, 1, 18, 9, 2, 1, 4, 4, 5, 2, 3, 1, 4, 2, 1, 2, 11, 2, 2, 1, 3, 2, 1, 1, 2, 4, 4, 6, 1, 4, 3, 4, 3

Offset

1,3

Comments

a(204) > 129000 if it is not -1. - Robert Israel, Mar 02 2026

Links

Robert Israel, Table of n, a(n) for n = 1..203

Formula

If A039739(k)=3 then a(k)=1. - Michel Marcus, Mar 02 2026

Example

(5 + 3^1)/2 = 4 = 9; (5 + 3^2)/2 = 7 (prime), so a(3) = 2.

Maple

f:= proc(n) local p, k;
 p:= ithprime(n);
 for k from 1 do if isprime((p+3^k)/2) then return k fi od:
end proc:
f(1):= -1:
map(f, [$1..203]); # Robert Israel, Mar 02 2026

Mathematica

f[n_] := Select[Range[100], PrimeQ[(Prime[n] + 3^#)/2] &, 1];
Join[{-1}, Flatten[Table[f[n], {n, 1, 120}]]]

Prog

(PARI) a(n) = if (n==1, -1, my(k=1, p=2); while (!ispseudoprime((prime(n) + 3^k)/2), k++); k); \\ Michel Marcus, Mar 02 2026

Crossrefs

Cf. A000040, A039739, A393710.

Sequence in context: A308188 A046219 A088978 * A276948 A160245 A154351

Adjacent sequences: A393706 A393707 A393708 * A393710 A393711 A393712

Keyword

sign

Author

Clark Kimberling, Mar 01 2026

Status

approved