A286660 a(n) = a(n-1) + sum of base-100 digits of a(n-1), a(0) = 1.

1, 2, 4, 8, 16, 32, 64, 128, 157, 215, 232, 266, 334, 371, 445, 494, 592, 689, 784, 875, 958, 1025, 1060, 1130, 1171, 1253, 1318, 1349, 1411, 1436, 1486, 1586, 1687, 1790, 1897, 2012, 2044, 2108, 2137, 2195, 2311, 2345, 2413, 2450, 2524, 2573, 2671, 2768, 2863, 2954, 3037, 3104, 3139

Offset: 0

Author

Peter Weiss, May 12 2017

Keywords

• nonn
• base

Examples

			a(7) = 128 = 1 * 100^1 + 28 * 100^0. The sum of digits of a(8 - 1) = 128 in base 100 is therefore 1 + 28 = 29. a(8) = a(7) + the sum of digits of a(7) in base 100 is therefore 128 + 29 = 157.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A004207, A010062.

Programs

Maple

g:= n -> n+convert(convert(n,base,100),`+`):
A[0]:= 1:
for n from 1 to 100 do A[n]:= g(A[n-1]) od:
seq(A[i],i=0..100); # Robert Israel, May 22 2017

Mathematica

a[0] = 1; a[n_] := a[n] = a[n-1] + Total[IntegerDigits[a[n-1], 100]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, May 21 2017 *)
NestList[#+Total[IntegerDigits[#,100]]&,1,60] (* Harvey P. Dale, May 26 2019 *)

PARI

a(n) = if(n < 8, return(1<<(n-1))); my(r = cr = 128); for(i=8, n, while(cr > 0, r += cr % 100; cr \= 100); cr = r); r \\ David A. Corneth, May 15 2017