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

0,1

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for sequences related to final digits of numbers

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A303141 A246070 A202778 * A355499 A094244 A075447

Adjacent sequences: A025013 A025014 A025015 * A025017 A025018 A025019

Keyword

nonn,base,nice

Author

David W. Wilson

Status

approved