A259230 a(n) = smallest k such that (A115091(n)-k)! == -1 (mod A115091(n)^2).

1, 6, 1, 24, 64, 1, 384

Offset: 1

Author

Felix Fröhlich, Nov 08 2015

Keywords

• nonn
• hard
• more

Comments

The values of m in A115091.

A115091(n) is in A007540 iff a(n) = 1.

Examples

			a(2) = 6, because 6 is the smallest k such that (A115091(2)-k)! == -1 (mod A115091(2)^2), which yields the congruence (11-6)! == -1 (mod 11^2).
		

Crossrefs

Cf. A007540, A115091.

Programs

Mathematica

t = Select[Prime@ Range@ 120, AnyTrue[Range@ #, Function[m, Divisible[m! + 1, #^2]]] &]; Table[k = 1; While[Mod[(t[[n]] - k)!, t[[n]]^2] != t[[n]]^2 - 1, k++]; k, {n, 7}] (* Michael De Vlieger, Nov 10 2015, Version 10 *)

PARI

forprime(p=1, , for(k=1, p-1, if(Mod((p-k)!, p^2)==-1, print1(k, ", "); break({1}))))