A259497 - OEIS

%I #15 Aug 02 2015 05:21:52

%S 1,10,96,918,8778,83970,803652,7695702,73736351,706940003,6782083197,

%T 65107856455,625462980243,6012764576492,57843691102715,

%U 556865542063090,5364870125881211,51722954280818076,499024949301954326,4818086348226292202,46551954003050282966

%N a(n) = number of steps before A055641(num(i)) = 0, when num(i) = num(i-1) + A055641(num(i-1)) and num(0) = 10^n, where A055641(n) is the number of zero digits in n.

%H Hiroaki Yamanouchi, <a href="/A259497/b259497.txt">Table of n, a(n) for n = 1..100</a>

%e For example, when num(0) = 10^1 = 10, A055641(10) = 1. 10 + 1 = 11 and A055641(11) = 0. Therefore a(1) = 1, because the procedure has taken one step before A055641(num(i)) = 0.

%e a(2) begins with num(0) = 10^2 = 100.

%e 1: 100 + A055641(100) = 100 + 2 = 102.

%e 2: 102 + A055641(102) = 102 + 1 = 103.

%e .

%e .

%e 9: 109 + A055641(109) = 109 + 1 = 110.

%e 10: 110 + A055641(110) = 110 + 1 = 111.

%e At the next step, A055641(111) = 0, so the procedure takes ten steps before A055641(num(i)) = 0 and a(2) = 10.

%o (PARI) { b=10; digmx=10; for(ni=2,digmx, n=b^(ni-1); s=0; until(z==0, d=digits(n,b); z=sum(i=2,ni,if(d[i]==0,1,0)); n+=z; s++; ); print1(s-1,", "); ); }

%Y Cf. A055641.

%K nonn,base

%O 1,2

%A _Anthony Sand_, Jun 29 2015

%E a(12)-a(21) from _Hiroaki Yamanouchi_, Aug 02 2015