A050493 - OEIS

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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

(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: A249030 A358527 A257126 * A331851 A335607 A366192

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