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

1,2

Comments

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

Links

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

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

Example

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

Maple

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

Prog

(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

Crossrefs

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

Sequence in context: A139707 A139709 A221714 * A108779 A385753 A288336

Adjacent sequences: A309758 A309759 A309760 * A309762 A309763 A309764

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 15 2019

Status

approved