OFFSET

0,1

COMMENTS

a(n)=1 iff n+1 is prime. For n>1 n+a(n) is odd (for n>1 a(n) is odd iff n is even). a(11) is greater than 7000. a(m) for m = 12, 13, 14, 15, 16, 17 and 18 are 1, 54, 17, 2, 1, 1080, 1. 5^7954 + 7954 is a 5560-digit probable prime.

a(11) is greater than 8651. - Robert G. Wilson v, May 24 2004

a(11) is greater than 20165, so every prime of the form 11^m + m has more than 21000 digits. - Farideh Firoozbakht, Jun 10 2004

a(11) is greater than 80000. - T. D. Noe, Mar 07 2007

a(11) is greater than 190000. - T. D. Noe, Jul 31 2008

LINKS

Henri Lifchitz & Renaud Lifchitz, 11^1181716+1181716, a(11).

Henri Lifchitz & Renaud Lifchitz, 19^57910+57910, a(19).

EXAMPLE

a(3)=2 because 3^2 + 2 is prime and 3^1 + 1 is composite.

MATHEMATICA

a[n_]:= (For[m=1, !PrimeQ[n^m+m], m++]; m); Do[Print[a[n]], {n, 0, 10}]

PROG

(Python)

from sympy import isprime

def a(n):

m = 0

while not isprime(n**m + m): m += 1

return m

for n in range(11):

print(a(n), end=", ") # Michael S. Branicky, Feb 01 2021

(Magma)

function A093324(n)

t:=0;

while not IsPrime(n^t + t) do

t+:=1;

end while;

return t;

end function;

[A093324(n): n in [0..10]]; // G. C. Greubel, Aug 10 2023

CROSSREFS

KEYWORD

nonn,hard,more

AUTHOR

Farideh Firoozbakht, May 11 2004

EXTENSIONS

a(11)-a(26) from Kellen Shenton, Aug 14 2023

STATUS

approved