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Smallest m such that (sum of binary digits of m*(m+1)/2) = n.
6

%I #19 Jan 27 2022 13:28:01

%S 0,1,2,6,5,10,19,22,37,77,108,165,90,313,461,620,1252,1957,2610,3237,

%T 5654,7797,9818,15797,22245,34725,56723,92634,122330,178540,226838,

%U 507571,454045,490426,1480005,2284378,1482842,2965594,5931098,10218573,11096982,21793257,31317157

%N Smallest m such that (sum of binary digits of m*(m+1)/2) = n.

%H Donovan Johnson, <a href="/A211201/b211201.txt">Table of n, a(n) for n = 0..71</a> (terms < 2*10^12)

%F A050493(a(n)) = n and A050493(m) <> n for m < a(n).

%o (Haskell)

%o import Data.List (elemIndex)

%o import Data.Maybe (fromJust)

%o a211201 = fromJust . (`elemIndex` a050493_list)

%o (PARI) a(n) = my(m=0); while (hammingweight(m*(m+1)/2) != n, m++); m; \\ _Michel Marcus_, Jan 27 2022

%Y Cf. A089999, A050493, A000217, A000120.

%K nonn,base

%O 0,3

%A _Reinhard Zumkeller_, Feb 04 2013