A340667 a(n) is derived from n by replacing each 0 in its binary representation with a string of n 0's.

0, 1, 4, 3, 256, 65, 192, 7, 16777216, 524289, 2098176, 8195, 50331648, 49153, 114688, 15, 18446744073709551616, 4503599627370497, 36028797019226112, 1099511627779, 2305844108725321728, 17592190238721, 70368756760576, 67108871, 14167099448608935641088

Offset: 0

Author

Alois P. Heinz, Jan 15 2021

Keywords

• nonn
• look
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Main diagonal of A340666.

Cf. A000079, A000120, A000225, A023416, A057156.

Programs

Maple

a:= n-> Bits[Join](subs(0=[0$n][], Bits[Split](n))):
seq(a(n), n=0..25);
# second Maple program:
b:= proc(n, k) option remember; `if`(n<2, n,
     `if`(irem(n, 2, 'r')=1, b(r, k)*2+1, b(r, k)*2^k))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);

Python

def A340667(n):
    return 0 if n == 0 else int(bin(n)[2:].replace('0','0'*n),2) # Chai Wah Wu, Jan 29 2021

Formula

a(n) = n <=> n in { A000225 }.

a(n) = n^n <=> n in { A000079 }.

A000120(a(n)) = A000120(n).

A023416(a(n)) = n * A023416(n) for n >= 1.