A025016 - OEIS

%I #25 Jul 11 2023 19:43:44

%S 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,

%T 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,

%U 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

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

%C Reversed digits of 10-adic sum of all factorials.

%C 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

%H Alois P. Heinz, <a href="/A025016/b025016.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

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

%t 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_ *)

%o (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

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

%K nonn,base,nice

%O 0,1

%A _David W. Wilson_