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

Author

Rémy Sigrist, Jan 18 2018

Keywords

• nonn
• base

Comments

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

The corresponding sequence for the binary base is A080100.

Examples

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

Links

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

Crossrefs

Cf. A080100, A100910.

Programs

PARI

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

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.