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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
1, 10, 96, 918, 8778, 83970, 803652, 7695702, 73736351, 706940003, 6782083197, 65107856455, 625462980243, 6012764576492, 57843691102715, 556865542063090, 5364870125881211, 51722954280818076, 499024949301954326, 4818086348226292202, 46551954003050282966 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn,base
AUTHOR
Anthony Sand, Jun 29 2015
EXTENSIONS
a(12)-a(21) from Hiroaki Yamanouchi, Aug 02 2015
STATUS
approved

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Last modified April 22 21:44 EDT 2024. Contains 371906 sequences. (Running on oeis4.)