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A346149
a(n) is the least integer k > 1 such that n^k + n + 1 is prime, or 0 if there is no such k.
2
2, 2, 2, 0, 2, 2, 0, 2, 3, 0, 4, 2, 0, 2, 2, 0, 2, 3, 0, 2, 2, 0, 9, 2, 0, 4, 2, 0, 3, 3, 0, 3, 2, 0, 15, 4, 0, 2, 3, 0, 2, 3, 0, 3, 6, 0, 4, 3, 0, 2, 9, 0, 3, 2, 0, 3, 2, 0, 2, 3, 0, 2, 73, 0, 12, 2, 0, 595, 2, 0, 2, 4, 0, 3, 2, 0, 2, 2, 0, 2, 7, 0, 3, 30, 0, 21, 3, 0, 2, 2, 0, 7, 67, 0, 3
OFFSET
1,1
COMMENTS
a(n) = 0 if n == 1 (mod 3) and n > 1.
Conjecture: a(n) > 0 otherwise.
LINKS
EXAMPLE
a(9) = 3 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 i fi od:
end proc:
f(1):= 2:
map(f, [$1..100]);
PROG
(PARI) a(n) = if ((n>1) && ((n%3)==1), 0, my(k=2); while (!isprime(n^k+n+1), k++); k); \\ Michel Marcus, Jul 07 2021
(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 k
print([a(n) for n in range(1, 96)]) # Michael S. Branicky, Jul 08 2021
CROSSREFS
Sequence in context: A217864 A002100 A108352 * A215883 A277024 A317528
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jul 07 2021
STATUS
approved