A018799 -id:A018799 - cp's OEIS frontend

A155896 Least positive integer such that a(n)! starts with n, both written in base 6.

1, 2, 5, 4, 8, 3, 9, 26, 52, 18, 25, 10, 33, 53, 32, 15, 13, 20, 30, 5, 17, 42, 7, 4, 23, 43, 78, 50, 28, 113, 8, 44, 19, 334, 59, 100, 195, 27, 22, 14, 91, 172, 371, 16, 93, 9, 12, 102, 66, 26, 46, 95, 279, 303, 69, 331, 272, 52, 286, 79, 264, 298, 18, 21, 190, 104, 47, 138, 255

Offset: 1

M. F. Hasler, Feb 01 2009

			a(3) = 5 since 5!=120 is the least factorial to start with digit "3" when written in base 6. a(8) = 26 since 8 = 12[6] (i.e. written in base 6) and 26! is the smallest factorial to start with digits "12" when written in base 6.

Cf. A155891--A155894, A018799, A076219.

A155896(n)={ local( F=1,k=1 ); while( F\1!=n, F*=k++; while( F>=n+1, F/=6)); k}

A197423 Smallest integer m such that !m begins with n in base 10.

Original entry on oeis.org

1, 0, 3, 14, 5, 25, 69, 16, 20, 4, 34, 28, 41, 9, 8, 53, 73, 12, 7, 38, 46, 81, 13, 18, 120, 138, 6, 156, 186, 52, 31, 33, 14, 166, 98, 97, 96, 104, 35, 105, 27, 22, 93, 146, 5, 48, 55, 249, 15, 91, 37, 42, 187, 77, 90, 124, 352, 25, 110, 394, 89, 280, 69, 147

Offset: 0

Michel Lagneau, Oct 14 2011

!n is a subfactorial number (A000166).

			Subfactorial(0) = 1 begins with 1, so a(1) = 0 ;
Subfactorial(3) = 2 begins with 2, so a(2) = 3 ;
Subfactorial(14) = 32071101049 begins with 3, so a(3) = 14.

Cf. A000166, A018799.

for n from 1 to 100 do:l1:=length(n):i:=0:for m from 1 to 400 while(i=0)do:
s:=0:for j from 0 to m do: s:=s+m!*(((-1)^j)*1/j!) :od:x:=s:l:=length(x):y:=floor(x/(10^(l-l1))):if y=n and l>=l1 then i:=1: printf ( "%d %d \n",n,m): else fi:od:od:

f[n_] := Block[{k = 0, m}, While[m = Max[0, Floor@Log[10, Subfactorial[k]] - Floor@Log[10, n]]; (Subfactorial[k] - Mod[Subfactorial[k], 10^m])/10^m! = n, k++]; k]; Array[f, 67] (* program from David W. Wilson - see A018799 Nov 05 2010 *)

a(0)=1 prepended by Alois P. Heinz, Feb 02 2017

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A155896 Least positive integer such that a(n)! starts with n, both written in base 6.

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A197423 Smallest integer m such that !m begins with n in base 10.

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