A259497 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.

1, 10, 96, 918, 8778, 83970, 803652, 7695702, 73736351, 706940003, 6782083197, 65107856455, 625462980243, 6012764576492, 57843691102715, 556865542063090, 5364870125881211, 51722954280818076, 499024949301954326, 4818086348226292202, 46551954003050282966

Offset

1,2

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100

Example

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.
a(2) begins with num(0) = 10^2 = 100.
1: 100 + A055641(100) = 100 + 2 = 102.
2: 102 + A055641(102) = 102 + 1 = 103.
.
.
9: 109 + A055641(109) = 109 + 1 = 110.
10: 110 + A055641(110) = 110 + 1 = 111.
At the next step, A055641(111) = 0, so the procedure takes ten steps before A055641(num(i)) = 0 and a(2) = 10.

Prog

(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, ", "); ); }

Crossrefs

Cf. A055641.

Sequence in context: A197086 A278359 A125945 * A190986 A287831 A288430

Adjacent sequences: A259494 A259495 A259496 * A259498 A259499 A259500

Keyword

nonn,base

Author

Anthony Sand, Jun 29 2015

Extensions

a(12)-a(21) from Hiroaki Yamanouchi, Aug 02 2015

Status

approved