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A089999 Smallest triangular number with Hamming weight n (i.e., with exactly n 1's when written in binary).

%I A089999 #16 Mar 29 2015 13:09:36
%S A089999 0,1,3,21,15,55,190,253,703,3003,5886,13695,4095,49141,106491,192510,
%T A089999 784378,1915903,3407355,5240703,15986685,30400503,48201471,124780503,
%U A089999 247431135,602930175,1608777726,4290575295,7482375615,15938355070
%N A089999 Smallest triangular number with Hamming weight n (i.e., with exactly n 1's when written in binary).
%C A089999 A000120(a(n)) = n.
%C A089999 a(n) = A000217(A211201(n)). - _Reinhard Zumkeller_, Mar 18 2013
%H A089999 Donovan Johnson, <a href="/A089999/b089999.txt">Table of n, a(n) for n = 0..60</a>
%t A089999 a = Table[0, {30}]; Do[t = n(n + 1)/2; c = Count[ IntegerDigits[t, 2], 1]; If[ a[[c + 1]] == 0, a[[c + 1]] = t], {n, 1, 10^8}]; a (* _Robert G. Wilson v_, Dec 03 2003 *)
%o A089999 (Haskell)
%o A089999 a089999 = a000217 . a211201  -- _Reinhard Zumkeller_, Mar 18 2013
%Y A089999 Cf. A211201, A000217, A089998, A061712, A090002.
%K A089999 nonn,base
%O A089999 0,3
%A A089999 _Reinhard Zumkeller_, Nov 20 2003
%E A089999 More terms from _Robert G. Wilson v_, Dec 03 2003
%E A089999 Offset corrected by _Donovan Johnson_, May 01 2012