A277830 Number of digits '0' in the set of all numbers from 0 to A014824(n) = Sum_{i=1..n} i*10^(n-i) = (0, 1, 12, 123, 1234, 12345, ...).

1, 1, 2, 23, 344, 4665, 58986, 713307, 8367628, 96021949, 1083676272, 12071330614, 133058985146, 1454046641578, 15775034317010, 170096022182442, 1824417011947874, 19478738020713306, 207133059219478738, 2194787382318244170, 23182441724417009624, 244170096256515775267

Offset: 0

Author

M. F. Hasler, Nov 01 2016

Keywords

• nonn
• base
• easy

Comments

The first 10 terms are given by a simple explicit formula and linear recurrence, which does not hold for n > 9. Note that A007908 (concat(1..n)) differs from A014824 (a(n) = a(n-1)*10 + n) for n > 9. - M. F. Hasler, Nov 07 2020

Links

• M. F. Hasler, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A277831 - A277838, A277849, A277635, A272525, A083449, A014824.

Programs

PARI

print1(c=1);N=0;for(n=1,8,print1(","c+=sum(k=N+1,N=N*10+n,#select(d->d==0,digits(k))))) \\ For purpose of illustration.

PARI

apply( A277830(n)={A061217(A014824(n)+!n)+1}, [0..22]) \\ Thanks to Kevin Ryde's formula. - M. F. Hasler, Nov 07 2020

Formula

a(n) = A083449(n) + 1 for n <= 9.

a(n) = 1 + A061217(A014824(n)), taking A061217(0)=0. - Kevin Ryde, Nov 07 2020

Extensions

Incorrect data, b-file, links, formulas and programs deleted by M. F. Hasler, following observations by Kevin Ryde, Nov 07 2020