A131954 a(n) = sum of digits of (n! + a(n-1)), with a(1)=1.

1, 3, 9, 6, 9, 18, 18, 18, 36, 36, 45, 36, 36, 54, 54, 72, 72, 63, 54, 63, 72, 81, 108, 90, 81, 90, 117, 99, 144, 126, 144, 117, 153, 153, 153, 180, 162, 117, 198, 207, 153, 198, 198, 234, 216, 225, 234, 243, 234, 225, 207, 288, 297, 279, 297, 351, 279, 306, 333, 297

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 31 2007

Keywords

• easy
• nonn
• base

Comments

If n >= 5, then 9 divides a(n); see comment in A004152. - Bernard Schott, Jun 27 2019

Examples

			a(4) = Sum_digits(4!+9) = 6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A004152, A055263, A131955.

Programs

Maple

P:=proc(n) local a,i,k,w; a:=0; for i from 1 by 1 to n do w:=0; k:=a+i!; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; a:=w; print(a); od; end: P(100);
# alternative:
sd:= n-> convert(convert(n,base,10),`+`):
A[1]:= 1:
for n from 2 to 100 do A[n]:= sd(n!+A[n-1]) od:
seq(A[i],i=1..100); # Robert Israel, Jun 26 2019

Mathematica

s={1};Do[AppendTo[s,DigitSum[n!+s[[-1]]]],{n,2,60}];s (* James C. McMahon, Mar 03 2025 *)

Formula

a(n) = Sum_digits(n!+a(n-1)).

Extensions

Offset corrected by Robert Israel, Jun 26 2019