A104258 Replace 2^i with n^i in binary representation of n.

1, 2, 4, 16, 26, 42, 57, 512, 730, 1010, 1343, 1872, 2367, 2954, 3616, 65536, 83522, 104994, 130341, 160400, 194923, 234762, 280394, 345600, 406251, 474578, 551152, 637392, 732512, 837930, 954305, 33554432, 39135394, 45435458

Offset: 1

Author

Ralf Stephan, Mar 05 2005

Keywords

• nonn
• base

Comments

The following sequences all appear to have the same parity: A003071, A029886, A061297, A092524, A093431, A102393, A104258, A122248, A128975. - Jeremy Gardiner, Dec 28 2008

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A104257.

Programs

PARI

a(n) = my(b=binary(n)); sum(k=1, #b, b[k]*n^(#b-k)); \\ Michel Marcus, Mar 19 2015

Python

def a(n): return sum(n**i*int(bi) for i, bi in enumerate(bin(n)[2:][::-1]))
print([a(n) for n in range(1, 35)]) # Michael S. Branicky, Aug 02 2022

Formula

a(n) = A104257(n, n).

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=0} n^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Aug 17 2019