A381041 Smallest prime p such that 3^n + p + 1 is prime.
3, 3, 3, 3, 7, 7, 3, 19, 7, 3, 3, 19, 79, 7, 7, 43, 67, 139, 127, 103, 7, 97, 3, 31, 31, 13, 379, 61, 109, 433, 3, 79, 127, 79, 67, 139, 127, 229, 7, 109, 271, 313, 3, 151, 7, 103, 67, 283, 421, 67, 43, 373, 97, 97, 97, 19, 61, 3, 157, 331, 127, 37, 139, 439, 421
Offset: 0
Keywords
Examples
a(0) = 3, since 3 + (3^0+1) = 5 is prime and 2 + (3^0+1) = 4 is not. a(1) = 3, since 3 + (3^1+1) = 7 is prime and 2 + (3^1+1) = 6 is not.
Links
- Robert Israel, Table of n, a(n) for n = 0..2000
Programs
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Maple
f:= proc(n) local t,p; p:= 1: t:= 3^n+1; do p:= nextprime(p); if isprime(p+t) then return p fi od; end proc: map(f, [$0..100]); # Robert Israel, Jun 19 2025
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Mathematica
a[n_]:=Module[{p=2},While[!PrimeQ[p+3^n+1], p=NextPrime[p]]; p]; Array[a,65,0] (* Stefano Spezia, Apr 25 2025 *) -
PARI
a(n) = my(p=2, x=3^n+1); while (!isprime(p+x), p=nextprime(p+1)); p; \\ Michel Marcus, Apr 24 2025
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Python
from sympy import isprime, nextprime def a(n): p, b = 2, 3**n+1 while not isprime(p+b): p = nextprime(p) return p print([a(n) for n in range(65)]) # Michael S. Branicky, Apr 23 2025 -
Python
from sympy import nextprime, isprime def A381041(n): p = 3**n+1 q = nextprime(p) while not isprime(q-p): q = nextprime(q) return q-p # Chai Wah Wu, May 01 2025
Formula
Extensions
More terms from Michael S. Branicky, Apr 23 2025