A050493 a(n) = sum of binary digits of n-th triangular number.

0, 1, 2, 2, 2, 4, 3, 3, 2, 4, 5, 2, 4, 5, 4, 4, 2, 4, 5, 6, 4, 6, 7, 3, 4, 4, 7, 6, 5, 6, 5, 5, 2, 4, 5, 6, 5, 8, 6, 4, 5, 7, 6, 6, 8, 4, 5, 4, 4, 5, 8, 6, 5, 7, 7, 3, 6, 7, 8, 7, 6, 7, 6, 6, 2, 4, 5, 6, 5, 8, 7, 8, 4, 6, 8, 5, 8, 9, 4, 5, 5, 8, 7, 8, 8, 7, 8, 8, 7, 8, 12, 5, 6, 5, 6, 5, 4, 5, 8, 7, 8

Offset: 0

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 27 1999

Keywords

• base
• easy
• nice
• nonn

Comments

See A211201 for smallest numbers m such that a(m) = n. - Reinhard Zumkeller, Feb 04 2013

Links

• T. D. Noe, Table of n, a(n) for n = 0..1024
• Index entries for Colombian or self numbers and related sequences
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A000217, A004157.

Programs

Haskell

a050493 = a000120 . a000217  -- Reinhard Zumkeller, Feb 04 2013

Mathematica

f[n_]:=Plus@@IntegerDigits[n,2]; lst={};Do[t=n*(n+1)/2;AppendTo[lst,f[t]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 10 2009 *)
Total[IntegerDigits[#,2]]&/@Accumulate[Range[0,100]] (* Harvey P. Dale, Jan 22 2012 *)

PARI

a(n)=hammingweight(n*(n+1)) \\ Charles R Greathouse IV, Nov 10 2015

Formula

a(n) = Sum_{i=1..floor(log_b(c(n)))+1} (floor(c(n)/b^(i-1)) - floor(c(n)/b^i)*b), b=2, n >= 1, a(0)=0, c(n)=A000217(n).

a(n) = A000120(A000217(n)). - Reinhard Zumkeller, Feb 04 2013

a(n) = [x^(n*(n+1)/2)] (1/(1 - x))*Sum_{k>=0} x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Mar 27 2018