A286660 - OEIS

%I #30 Jan 17 2024 09:12:04

%S 1,2,4,8,16,32,64,128,157,215,232,266,334,371,445,494,592,689,784,875,

%T 958,1025,1060,1130,1171,1253,1318,1349,1411,1436,1486,1586,1687,1790,

%U 1897,2012,2044,2108,2137,2195,2311,2345,2413,2450,2524,2573,2671,2768,2863,2954,3037,3104,3139

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

%H Robert Israel, <a href="/A286660/b286660.txt">Table of n, a(n) for n = 0..10000</a>

%e 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.

%p g:= n -> n+convert(convert(n,base,100),`+`):

%p A[0]:= 1:

%p for n from 1 to 100 do A[n]:= g(A[n-1]) od:

%p seq(A[i],i=0..100); # _Robert Israel_, May 22 2017

%t a[0] = 1; a[n_] := a[n] = a[n-1] + Total[IntegerDigits[a[n-1], 100]];

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, May 21 2017 *)

%t NestList[#+Total[IntegerDigits[#,100]]&,1,60] (* _Harvey P. Dale_, May 26 2019 *)

%o (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

%Y Cf. A004207, A010062.

%K nonn,base

%O 0,2

%A _Peter Weiss_, May 12 2017