A298372 a(n), in decimal base, is the number of numbers k >= 0 with no more digits than n such that k + n can be computed without carry.

1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 90, 81, 72, 63, 54, 45, 36, 27, 18, 9, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8, 70, 63, 56, 49, 42, 35, 28, 21, 14, 7, 60, 54, 48, 42, 36, 30, 24, 18, 12, 6, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 40, 36, 32, 28, 24, 20, 16, 12, 8

Offset

0,2

Comments

We consider here that 0 has no digit, and hence a(0) = 1.

The corresponding sequence for the binary base is A080100.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9999

Formula

a(0) = 1.

a(10 * k + d) = a(k) * (10 - d) when 10 * k + d > 0 and 0 <= d < 10.

a(n) = Product_{ d = 0..9 } (10 - d)^A100910(n, d) for any n > 0.

Example

a(42) = (10 - 4) * (10 - 2) = 48.

Prog

(PARI) a(n, {base=10}) = my (d=digits(n, base)); prod(i=1, #d, base-d[i])

Crossrefs

Cf. A080100, A100910.

Sequence in context: A087029 A104348 A251984 * A089186 A055120 A342115

Adjacent sequences: A298369 A298370 A298371 * A298373 A298374 A298375

Keyword

nonn,base

Author

Rémy Sigrist, Jan 18 2018

Status

approved