A025016 Final digits of !n = Sum_{i=0..n} i! (A003422) for very large n, read from right.

4, 1, 3, 0, 4, 9, 0, 2, 4, 0, 2, 9, 8, 2, 5, 6, 3, 3, 2, 4, 4, 6, 5, 5, 2, 5, 0, 9, 3, 0, 5, 0, 1, 3, 9, 5, 3, 2, 3, 4, 0, 8, 4, 9, 9, 7, 0, 1, 1, 2, 6, 8, 3, 7, 4, 8, 6, 8, 7, 4, 9, 7, 4, 7, 4, 2, 2, 9, 0, 0, 4, 3, 3, 0, 5, 6, 5, 8, 6, 5, 0, 0, 2, 6, 6, 5, 1, 5, 9, 7, 8, 8, 1, 6, 2, 0, 2, 8, 1, 2, 1, 3, 7, 6, 1, 1, 5, 8

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base
• nice

Comments

Reversed digits of 10-adic sum of all factorials.

More generally, the 10-adic sum: B(n) = Sum_{k>=0} k^n*k! is given by: B(n) = A014182(n)*B(0) + A014619(n) for n>=0, where B(0) is the 10-adic sum of factorials (this constant). - Paul D. Hanna, Aug 12 2006

Examples

			!20 = 256132749111820314, !30 = 16158688114800553828940314 ... .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to final digits of numbers

Crossrefs

Cf. A000142, A003422, A014182, A014619, A065356.

Programs

Mathematica

a[n_] := Module[{x, f=1}, While[Mod[f!, 10^(n+1)]>0, f += 1]; x = Sum[ Mod[k!, 10^(n+1)], {k, 0, f}]; Quotient[10*Mod[x, 10^(n+1)], 10^(n+1)]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 18 2015, after Paul D. Hanna *)

PARI

{a(n)=local(x,f=1);while(f!%10^(n+1)>0,f+=1); x=sum(k=0,f,k!%10^(n+1));(10*(x%10^(n+1)))\10^(n+1)} \\ Paul D. Hanna, Aug 12 2006