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Numbers that are sums of consecutive powers of 10.
4

%I #13 Aug 17 2019 03:26:47

%S 1,10,11,100,110,111,1000,1100,1110,1111,10000,11000,11100,11110,

%T 11111,100000,110000,111000,111100,111110,111111,1000000,1100000,

%U 1110000,1111000,1111100,1111110,1111111,10000000,11000000,11100000,11110000,11111000,11111100

%N Numbers that are sums of consecutive powers of 10.

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

%H Robert Israel, <a href="/A309761/b309761.txt">Table of n, a(n) for n = 1..10011</a>

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

%F a(i*(i-1)/2 + j) = (10^i - 10^(i-j))/9 for 1<=j<=i. - _Robert Israel_, Aug 16 2019

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

%p seq(seq((10^i-10^(i-j))/9, j=1..i),i=1..10); # _Robert Israel_, Aug 16 2019

%Y Cf. A000042, A007088, A011557, A023758, A038444, A309758, A309759.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Aug 15 2019