A113539 a(n) is the minimal k such that 3^n +/- k are primes.

2, 4, 2, 14, 10, 26, 8, 80, 20, 20, 110, 64, 8, 16, 110, 106, 10, 280, 8, 166, 92, 364, 68, 310, 130, 836, 70, 364, 238, 434, 892, 1844, 58, 140, 10, 740, 482, 1274, 308, 494, 1220, 2644, 790, 646, 2248, 2456, 422, 314, 1072, 1124, 782, 200, 98, 1826, 1502

Offset

2,1

Links

Robert Israel, Table of n, a(n) for n = 2..1140

Formula

a(n) = A082467(3^n). - Robert Israel, Dec 24 2025

Example

First term (at n=2) is a(2)=2 because 3^2 +/- 2 are primes; second term (at n=3) is a(3)=4 because 3^3 +/- 4 are primes.

Maple

f:= proc(n) local t, k;
   t:= 3^n;
   for k from 2 by 2 do
     if isprime(t-k) and isprime(t+k) then return k fi
   od
end proc:
map(f, [$2..100]); # Robert Israel, Dec 24 2025

Mathematica

f[n_] := Block[{k = 2}, While[ !PrimeQ[3^n + k] || !PrimeQ[3^n - k], k += 2]; k]; Table[ f[n], {n, 2, 56}] (* Robert G. Wilson v, Jan 18 2006 *)
Table[Module[{k=1, c=3^n}, Until[AllTrue[c+{k, -k}, PrimeQ], k++]; k], {n, 2, 60}] (* Harvey P. Dale, Jul 19 2025 *)

Crossrefs

Cf. A082467.

Sequence in context: A062867 A384867 A264027 * A215055 A152877 A071353

Adjacent sequences: A113536 A113537 A113538 * A113540 A113541 A113542

Keyword

nonn

Author

Zak Seidov, Jan 13 2006

Extensions

Corrected and extended by Robert G. Wilson v, Jan 18 2006

Status

approved