1,4

This is one possible generalization of "the least prime problem" for n*k+1 arithmetic progression when n is replaced by n!, a special difference.

Table of n, a(n) for n=1..85.

Index entries for sequences related to primes in arithmetic progressions

a(7)=3 because in progression of 5040*k+1 the terms 5041 and 10081 are not prime and so 15121 is the first prime.

Table[k = 1; While[! PrimeQ[1 + k*n!], k++]; k, {n, 85}] (* T. D. Noe, Nov 04 2013 *)

(PARI) a(n) = my(k=1); while(!isprime(k*n!+1), k++); k; \\ Michel Marcus, Sep 26 2020

Analogous case is A034693. Special case for k=1 is A002981.

Sequence in context: A130970 A144733 A091460 * A292511 A238872 A260195

Adjacent sequences: A035090 A035091 A035092 * A035094 A035095 A035096

nonn

Labos Elemer

a(80) corrected by Alex Ratushnyak, Nov 03 2013

Simpler title by Sean A. Irvine, Sep 25 2020

approved