A392099 Smallest prime p such that p + 3^n - 1 is also a prime.

2, 3, 3, 3, 3, 29, 5, 17, 3, 5, 3, 71, 17, 17, 3, 3, 29, 89, 11, 137, 47, 167, 5, 107, 3, 29, 3, 17, 71, 131, 5, 17, 71, 71, 59, 23, 3, 197, 179, 83, 233, 71, 5, 53, 179, 47, 113, 53, 113, 17, 29, 113, 467, 257, 29, 53, 173, 5, 251, 1283, 17, 191, 149, 3, 257

Offset

0,1

Links

Table of n, a(n) for n=0..64.

James S. DeArmon, R Code for A392099

Example

a(0)=2, since 2+3^0-1 = 2, a prime.
a(1)=3, since 3+3^1-1 = 5, a prime.

Maple

a:= proc(n) option remember; local p, k; p, k:= 2, 3^n-1;
      while not isprime(p+k) do p:= nextprime(p) od; p
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Jan 04 2026

Mathematica

a[n_]:=Module[{p=2}, While[!PrimeQ[p+3^n-1], p=NextPrime[p]]; p]; Array[a, 61, 0] (* Stefano Spezia, Jan 04 2026 *)

Prog

(R) # See Links.

Crossrefs

Cf. A051783, A056206, A342502, A001359, A000040.

Sequence in context: A033679 A051670 A089702 * A089336 A089335 A088093

Adjacent sequences: A392096 A392097 A392098 * A392100 A392101 A392102

Keyword

nonn

Author

James S. DeArmon, Dec 30 2025

Status

approved