A389715 Smallest prime p such that p - 3^n + 1 is also a prime.

2, 5, 11, 29, 83, 271, 733, 2203, 6563, 19687, 59051, 177217, 531457, 1594339, 4782971, 14348909, 43046749, 129140251, 387420499, 1162261603, 3486784447, 10460353369, 31381059613, 94143178933, 282429536483, 847288609471, 2541865828331, 7625597485003, 22876792455031

Offset

0,1

Links

Table of n, a(n) for n=0..28.

James S. DeArmon, R Code for A389715

Formula

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

Example

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.

Maple

a:= proc(n) option remember; local p, k; p, k:= 3^n-1$2;
      while not isprime(p-k) do p:= nextprime(p) od; p
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jan 11 2026

Prog

(R) # See Links.

Crossrefs

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

Sequence in context: A320171 A014211 A395332 * A160911 A092764 A237811

Adjacent sequences: A389712 A389713 A389714 * A389716 A389717 A389718

Keyword

nonn

Author

James S. DeArmon, Jan 08 2026

Status

approved