A309761 Numbers that are sums of consecutive powers of 10.

1, 10, 11, 100, 110, 111, 1000, 1100, 1110, 1111, 10000, 11000, 11100, 11110, 11111, 100000, 110000, 111000, 111100, 111110, 111111, 1000000, 1100000, 1110000, 1111000, 1111100, 1111110, 1111111, 10000000, 11000000, 11100000, 11110000, 11111000, 11111100

Offset: 1

Author

Ilya Gutkovskiy, Aug 15 2019

Keywords

• nonn

Comments

Numbers of the form (10^i - 10^j)/9 with i > j.

Examples

			11100 = 10^2 + 10^3 + 10^4, so 11100 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10011

Crossrefs

Cf. A000042, A007088, A011557, A023758, A038444, A276349, A309758, A309759.

Programs

Maple

seq(seq((10^i-10^(i-j))/9, j=1..i),i=1..10); # Robert Israel, Aug 16 2019

Python

from math import isqrt
def A309761(n): return (10**(m:=isqrt(n<<3)+1>>1)-10**(m*(m+1)-(n<<1)>>1))//9 # Chai Wah Wu, Apr 04 2025

Formula

a(n) = A007088(A023758(n+1)).

a(i*(i-1)/2 + j) = (10^i - 10^(i-j))/9 for 1<=j<=i. - Robert Israel, Aug 16 2019

a(n) = A276349(n)/10. - Chai Wah Wu, Jun 16 2025