cp's OEIS Frontend

A309761 Numbers that are sums of consecutive powers of 10.

%I A309761 #21 Jun 16 2025 11:30:05
%S A309761 1,10,11,100,110,111,1000,1100,1110,1111,10000,11000,11100,11110,
%T A309761 11111,100000,110000,111000,111100,111110,111111,1000000,1100000,
%U A309761 1110000,1111000,1111100,1111110,1111111,10000000,11000000,11100000,11110000,11111000,11111100
%N A309761 Numbers that are sums of consecutive powers of 10.
%C A309761 Numbers of the form (10^i - 10^j)/9 with i > j.
%H A309761 Robert Israel, <a href="/A309761/b309761.txt">Table of n, a(n) for n = 1..10011</a>
%F A309761 a(n) = A007088(A023758(n+1)).
%F A309761 a(i*(i-1)/2 + j) = (10^i - 10^(i-j))/9 for 1<=j<=i. - _Robert Israel_, Aug 16 2019
%F A309761 a(n) = A276349(n)/10. - _Chai Wah Wu_, Jun 16 2025
%e A309761 11100 = 10^2 + 10^3 + 10^4, so 11100 is in the sequence.
%p A309761 seq(seq((10^i-10^(i-j))/9, j=1..i),i=1..10); # _Robert Israel_, Aug 16 2019
%o A309761 (Python)
%o A309761 from math import isqrt
%o A309761 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
%Y A309761 Cf. A000042, A007088, A011557, A023758, A038444, A276349, A309758, A309759.
%K A309761 nonn
%O A309761 1,2
%A A309761 _Ilya Gutkovskiy_, Aug 15 2019