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A095194 Least number that yields a semiprime when appended to n!. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)