cp's OEIS Frontend

A068129 Triangular numbers with sum of digits = 10.

%I A068129 #18 May 15 2025 14:21:06
%S A068129 28,55,91,136,190,253,325,406,703,820,1081,1225,1540,1711,2080,2701,
%T A068129 3160,3403,5050,7021,10153,11026,12403,15400,17020,20503,21115,23005,
%U A068129 24310,32131,41041,51040,52003,60031,72010,80200,90100,106030,110215
%N A068129 Triangular numbers with sum of digits = 10.
%C A068129 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 A068129 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
%H A068129 Robert Israel, <a href="/A068129/b068129.txt">Table of n, a(n) for n = 1..164</a>
%p A068129 for i from 1 to 9 do S[1,i]:= [i] od: S[1,10]:= []:
%p A068129 R:= NULL: count:= 0:
%p A068129 for d from 2 while count < 100 do
%p A068129   for i from 1 to 10 do
%p A068129     S[d,i]:= [seq(op(map(t -> 10*t + j, S[d-1,i-j])),j=0..i-1)];
%p A068129   od:
%p A068129   V:= select(t -> issqr(8*t+1), S[d,10]);
%p A068129   if nops(V) > 0 then
%p A068129     V:= sort(V);
%p A068129     R:= R,op(V); count:= count+nops(V);
%p A068129   fi
%p A068129 od:
%p A068129 R; # _Robert Israel_, May 15 2025
%t A068129 Select[Accumulate[Range[1000]],Total[IntegerDigits[#]]==10&] (* _Harvey P. Dale_, Jun 07 2017 *)
%Y A068129 Intersection of A000217 and A052224.
%Y A068129 Cf. A062688, A068127, A068128.
%K A068129 base,easy,nonn
%O A068129 1,1
%A A068129 _Amarnath Murthy_, Feb 21 2002
%E A068129 More terms from _Sascha Kurz_, Mar 06 2002
%E A068129 Offset changed by _Andrew Howroyd_, Sep 17 2024