A392099 - OEIS

%I #21 Jan 08 2026 22:20:21

%S 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,

%T 3,17,71,131,5,17,71,71,59,23,3,197,179,83,233,71,5,53,179,47,113,53,

%U 113,17,29,113,467,257,29,53,173,5,251,1283,17,191,149,3,257

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

%H James S. DeArmon, <a href="/A392099/a392099.txt">R Code for A392099</a>

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

%e a(1)=3, since 3+3^1-1 = 5, a prime.

%p a:= proc(n) option remember; local p,k; p,k:= 2,3^n-1;

%p       while not isprime(p+k) do p:= nextprime(p) od; p

%p     end:

%p seq(a(n), n=0..100);  # _Alois P. Heinz_, Jan 04 2026

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

%o (R) # See Links.

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

%K nonn

%O 0,1

%A _James S. DeArmon_, Dec 30 2025