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URL: https://oeis.org/A245788

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A245788
n times the number of 1's in the binary expansion of n.
6
0, 1, 2, 6, 4, 10, 12, 21, 8, 18, 20, 33, 24, 39, 42, 60, 16, 34, 36, 57, 40, 63, 66, 92, 48, 75, 78, 108, 84, 116, 120, 155, 32, 66, 68, 105, 72, 111, 114, 156, 80, 123, 126, 172, 132, 180, 184, 235, 96, 147, 150, 204, 156, 212, 216, 275, 168, 228, 232, 295, 240
OFFSET
0,3
LINKS
Project Euler, Problem 759, sequence f(n).
FORMULA
a(2*n) = 2*a(n).
a(2*n+1) = 2*n + 1 + (2+1/n)*a(n). - Robert Israel, Aug 01 2014
G.f.: x * (d/dx) (1/(1 - x))*Sum_{k>=0} x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Mar 27 2018
EXAMPLE
G.f. = x + 2*x^2 + 6*x^3 + 4*x^4 + 10*x^5 + 12*x6 + 21*x^7 + 8*x^8 + 18*x^9 + ...
MAPLE
a:= n -> n * convert(convert(n, base, 2), `+`):
seq(a(n), n=0..100); # Robert Israel, Aug 01 2014
MATHEMATICA
Table[n*DigitCount[n, 2, 1], {n, 0, 100}] (* Harvey P. Dale, Dec 16 2014 *)
PROG
(PARI) sumbit(n) = my(r); while(n>0, r+=n%2; n\=2); r
a(n) = n*sumbit(n)
(PARI) {a(n) = if( n<0, 0, n * sumdigits(n, 2))}; /* Michael Somos, Aug 05 2014 */ /* since version 2.6.0 */
(Python) [n*bin(n)[2:].count('1') for n in range(1000)] # Chai Wah Wu, Aug 03 2014
CROSSREFS
Cf. A000120 (number of 1's), A057147 (decimal version).
Sequence in context: A264647 A094748 A245579 * A065879 A065880 A335063
KEYWORD
nonn,base
AUTHOR
STATUS
approved