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

1,3

Comments

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

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..113, (terms a(1)-a(101) from Sean A. Irvine, a(102) from Florian Baur)

Example

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

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 *)

Prog

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

Crossrefs

Cf. A068845, A001358.

Sequence in context: A090986 A245221 A195726 * A254251 A095711 A102886

Adjacent sequences: A095191 A095192 A095193 * A095195 A095196 A095197

Keyword

base,nonn,hard

Author

Jason Earls, Jun 21 2004

Extensions

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

Status

approved