A095194 Least number that yields a semiprime when appended to n!.

0, 1, 2, 7, 2, 1, 1, 1, 1, 1, 2, 1, 1, 7, 17, 1, 1, 1, 31, 13, 1, 59, 13, 7, 1, 61, 41, 37, 31, 1, 7, 7, 1, 2, 5, 61, 41, 7, 13, 37, 61, 43, 1, 1, 47, 67, 1, 3, 67, 61, 5, 19, 5, 11, 7, 13, 1, 3, 1, 71, 11, 1, 67, 109, 103, 43, 29

Offset: 1

Author

Jason Earls, Jun 21 2004

Keywords

• base
• nonn
• hard

Comments

a(114) would require the factorization of the 190-digit number 1000*114!+181. - Hugo Pfoertner, May 18 2021

Examples

			Refers to the semiprimes 10, 21, 62, 247, 1202, 7201, 50401, 403201, etc.
		

Links

• Tyler Busby, Table of n, a(n) for n = 1..126 (terms 1..101 from Sean A. Irvine, term 102 from Florian Baur, terms 103..113 from Hugo Pfoertner)

Crossrefs

Cf. A068845, A001358.

Programs

Maple

A095194 := proc(n) local nf,i,ns ; nf := convert(n!,base,10) ; for i from 1 do ns := [op(convert(i,base,10)),op(nf)] ; add( op(j,ns)*10^(j-1),j=1..nops(ns)) ; if numtheory[bigomega](%) = 2 then return i ; end if; end do: end proc: # R. J. Mathar, Jun 17 2011

Mathematica

Array[Block[{m = #!, k = 0}, While[PrimeOmega[10^If[k == 0, 1, IntegerLength[k]]*m + k] != 2, k++]; k] &, 40] (* Michael De Vlieger, May 17 2021 *)

PARI

a(n)=for(i=0,1e9,bigomega(eval(Str(n!,i)))==2 & return(i))  \\ M. F. Hasler, Jun 17 2011

Extensions

Corrected and extended by Sean A. Irvine, Jun 16 2011