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%I #19 Sep 09 2017 22:34:49
%S 11,22,33,44,55,66,77,88,99,505,550,5005,5050,5500,5555,50005,50050,
%T 50500,50555,55000,55055,55505,55550,500005,500050,500500,500555,
%U 505000,505055,505505,505550,550000,550055,550505,550550,555005,555050,555500,555555,1111116
%N Numbers in which each digit equals the sum (mod 10) of the other digits.
%C The primitive terms in this sequence are 11, 22, 33, 44, 55, 66, 77, 88, 99, 505, 5005, 5555, 50005, 50555, 500005, 500555, 555555, 1111116, 1111666, 1166666, 2222222, 2222277, ...; the other terms are built from the permutations of the digits of these numbers.
%C We find the following subsequences:
%C 505, 5005, 50005, 500005, ..., 5000000005;
%C 55, 5555, 555555, 55555555, ..., 5555555555.
%e 505 is in the sequence because the digits 5,0,5 satisfy
%e 5 = (0 + 5) mod 10;
%e 0 = (5 + 5) mod 10;
%e 5 = (5 + 0) mod 10.
%t Select[Range[10^5], IntegerDigits[#] == Mod[Total[IntegerDigits[#]] - IntegerDigits[#], 10] &]
%Y Cf. A007953, A053837.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Jun 08 2013
%E Edited by _Jon E. Schoenfield_, Sep 09 2017