A197354 a(n) = Sum_{k>=0} A030308(n,k)*(2k+1).

0, 1, 3, 4, 5, 6, 8, 9, 7, 8, 10, 11, 12, 13, 15, 16, 9, 10, 12, 13, 14, 15, 17, 18, 16, 17, 19, 20, 21, 22, 24, 25, 11, 12, 14, 15, 16, 17, 19, 20, 18, 19, 21, 22, 23, 24, 26, 27, 20, 21, 23, 24, 25, 26, 28, 29, 27, 28, 30, 31, 32, 33, 35, 36, 13, 14, 16

Offset: 0

Author

Philippe Deléham, Oct 14 2011

Keywords

• easy
• nonn

Comments

For any k >= 0, A000700(k) equals the number of occurrences of k in the sequence. - Rémy Sigrist, Jan 19 2019

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192

Crossrefs

Cf. A000700, A005408, A030308.

Other sequences that are built by replacing 2^k in the binary representation with other numbers: A022290 (Fibonacci), A029931 (natural numbers), A059590 (factorials), A089625 (primes).

Programs

PARI

a(n) = my (b=Vecrev(binary(n))); sum(i=1, #b, if (b[i], 2*i-1, 0)) \\ Rémy Sigrist, Jan 19 2019

Formula

a(2^n-1) = n^2.

a(n) mod 2 = A010060(n).

G.f.: (1/(1 - x))*Sum_{k>=0} (2*k + 1)*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jul 23 2017