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A346154
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a(n) is the least prime of the form n^k+n+1 with k>1, or 0 if there is no such prime.
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2
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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
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OFFSET
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1,1
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COMMENTS
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a(n) = 0 if n == 1 (mod 3) and n > 1.
Conjecture: a(n) > 0 otherwise.
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..67
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FORMULA
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a(n) = n^A346149(n) + n + 1 if A346149(n) > 0.
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EXAMPLE
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a(9) = 739 because 9^3 + 9 + 1 = 739 is prime while 9^2 + 9 + 1 is not.
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MAPLE
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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]);
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PROG
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(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
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CROSSREFS
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Cf. A346149.
Sequence in context: A096856 A345260 A108154 * A010260 A258136 A209387
Adjacent sequences: A346149 A346152 A346153 * A346156 A346157 A346158
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KEYWORD
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nonn,new
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AUTHOR
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J. M. Bergot and Robert Israel, Jul 07 2021
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STATUS
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approved
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