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Triangular numbers with sum of digits = 6.
6

%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