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A050493 a(n) = sum of binary digits of n-th triangular number. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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

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 *)

PROG

(Haskell)

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

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

CROSSREFS

Cf. A000120, A000217, A004157.

Sequence in context: A208609 A249030 A257126 * A085454 A083403 A114091

Adjacent sequences:  A050490 A050491 A050492 * A050494 A050495 A050496

KEYWORD

base,easy,nice,nonn

AUTHOR

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

STATUS

approved

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Last modified September 20 06:17 EDT 2019. Contains 327212 sequences. (Running on oeis4.)