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%I #12 Sep 17 2024 19:06:11
%S 28,55,91,136,190,253,325,406,703,820,1081,1225,1540,1711,2080,2701,
%T 3160,3403,5050,7021,10153,11026,12403,15400,17020,20503,21115,23005,
%U 24310,32131,41041,51040,52003,60031,72010,80200,90100,106030,110215
%N Triangular numbers with sum of digits = 10.
%C 1. The sequence is unbounded, as the (2*10^k +2)-th triangular number is a term. 2. The sum of the digits of triangular numbers in most cases is a triangular number. 3. Conjecture: For every triangular number T there exist infinitely many triangular numbers with sum of digits = T.
%C The second assertion above is wrong. Out of the first 100,000 triangular numbers, only 26,046 have a sum of their digits equal to a triangular number. - _Harvey P. Dale_, Jun 07 2017
%t Select[Accumulate[Range[1000]],Total[IntegerDigits[#]]==10&] (* _Harvey P. Dale_, Jun 07 2017 *)
%Y Intersection of A000217 and A052224.
%Y Cf. A068127, A068128.
%K base,easy,nonn,changed
%O 1,1
%A _Amarnath Murthy_, Feb 21 2002
%E More terms from _Sascha Kurz_, Mar 06 2002
%E Offset changed by _Andrew Howroyd_, Sep 17 2024