A346154 a(n) is the least prime of the form n^k+n+1 with k>1, or 0 if there is no such prime.

3, 7, 13, 0, 31, 43, 0, 73, 739, 0, 14653, 157, 0, 211, 241, 0, 307, 5851, 0, 421, 463, 0, 1801152661487, 601, 0, 457003, 757, 0, 24419, 27031, 0, 32801, 1123, 0, 144884079282928466796911, 1679653, 0, 1483, 59359, 0, 1723, 74131, 0, 85229, 8303765671, 0, 4879729, 110641, 0, 2551, 2334165173090503

Offset

1,1

Comments

a(n) = 0 if n == 1 (mod 3) and n > 1.

Conjecture: a(n) > 0 otherwise.

Links

Robert Israel, Table of n, a(n) for n = 1..67

Formula

a(n) = n^A346149(n) + n + 1 if A346149(n) > 0.

Example

a(9) = 739 because 9^3 + 9 + 1 = 739 is prime while 9^2 + 9 + 1 is not.

Maple

f:= proc(n) local i;
if n mod 3 = 1 then return 0 fi;
for i from 2 do if isprime(n^i+n+1) then return n^i+n+1 fi od:
end proc:
f(1):= 3:
map(f, [$1..100]);

Prog

(Python)
from sympy import isprime
def a(n):
    if n > 1 and n%3 == 1: return 0
    k = 2
    while not isprime(n**k + n + 1): k += 1
    return n**k + n + 1
print([a(n) for n in range(1, 52)]) # Michael S. Branicky, Jul 07 2021

Crossrefs

Cf. A346149.

Sequence in context: A347862 A345260 A108154 * A010260 A366999 A258136

Adjacent sequences: A346151 A346152 A346153 * A346155 A346156 A346157

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 07 2021

Status

approved