A389715 - OEIS

%I #20 Jan 14 2026 14:32:57

%S 2,5,11,29,83,271,733,2203,6563,19687,59051,177217,531457,1594339,

%T 4782971,14348909,43046749,129140251,387420499,1162261603,3486784447,

%U 10460353369,31381059613,94143178933,282429536483,847288609471,2541865828331,7625597485003,22876792455031

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

%H James S. DeArmon, <a href="/A389715/a389715.txt">R Code for A389715</a>

%F a(n) = A392099(n) + 3^n - 1 = A392099(n) + A024023(n).

%e a(0)=2, since: A392099(0) is 2, and the second number in the pair is 2+3^0-1=2. a(1)=5, since A392099(1) is 5, and the second number in the pair is 3+3^1-1=5.

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

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

%p     end:

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Jan 11 2026

%o (R) # See Links.

%Y Cf. A024023, A392099, A006512, A051783, A056206, A342502, A001359, A000040.

%K nonn

%O 0,1

%A _James S. DeArmon_, Jan 08 2026