A068845 -id:A068845 - cp's OEIS frontend

A068844 Smallest prime with same leading digits as n!.

11, 23, 61, 241, 1201, 7207, 504001, 4032029, 36288017, 362880043, 3991680029, 47900160013, 622702080047, 8717829120019, 130767436800073, 2092278988800037, 35568742809600019, 640237370572800041

Offset: 1

Amarnath Murthy, Mar 10 2002

			a(7) = 504011 because this is the smallest prime starting with 7! = 5040.

Cf. A068845.

for i from 1 to 40 do a := nextprime(i!*10); b := 1; while(a-i!*10^b>=10^b) do b := b+1; a := nextprime(i!*10^b); end do; c[i] := a; end do:q := seq(c[i],i=1..40);

Table[p = i!; k = 1; While[IntegerDigits[p] != Take[IntegerDigits[x = NextPrime[p*10^k]], IntegerLength[p]], k += 1]; x, {i, 18}] (* Jayanta Basu, Aug 09 2013 *)

More terms from Sascha Kurz, Mar 17 2002

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

Original entry on oeis.org

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

Jason Earls, Jun 21 2004

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

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

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)

Cf. A068845, A001358.

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

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 *)

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

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

cp's OEIS Frontend

A068844 Smallest prime with same leading digits as n!.

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