%I #14 Sep 17 2024 19:06:39
%S 6,15,105,231,2211,3003,20301,112101,2003001,122000010,200030001,
%T 20000300001,2000003000001,200000030000001,20000000300000001,
%U 2000000003000000001,200000000030000000001,20000000000300000000001,2000000000003000000000001
%N Triangular numbers with sum of digits = 6.
%C 1. The sequence is unbounded, as the (2*10^k +1)-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.
%t Select[Accumulate[Range[20000002]],Total[IntegerDigits[#]]==6&] (* _Harvey P. Dale_, Jun 05 2012 *)
%Y Intersection of A000217 and A052220.
%Y Cf. A068127.
%K base,easy,nonn
%O 1,1
%A _Amarnath Murthy_, Feb 21 2002
%E More terms from _Sascha Kurz_, Mar 06 2002
%E More terms from _Sean A. Irvine_, Mar 17 2023
%E Offset changed by _Andrew Howroyd_, Sep 17 2024