A340667 - OEIS

%I #20 Jan 29 2021 18:58:02

%S 0,1,4,3,256,65,192,7,16777216,524289,2098176,8195,50331648,49153,

%T 114688,15,18446744073709551616,4503599627370497,36028797019226112,

%U 1099511627779,2305844108725321728,17592190238721,70368756760576,67108871,14167099448608935641088

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

%H Alois P. Heinz, <a href="/A340667/b340667.txt">Table of n, a(n) for n = 0..500</a>

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

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

%F A000120(a(n)) = A000120(n).

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

%p a:= n-> Bits[Join](subs(0=[0$n][], Bits[Split](n))):

%p seq(a(n), n=0..25);

%p # second Maple program:

%p b:= proc(n, k) option remember; `if`(n<2, n,

%p      `if`(irem(n, 2, 'r')=1, b(r, k)*2+1, b(r, k)*2^k))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..25);

%o (Python)

%o def A340667(n):

%o     return 0 if n == 0 else int(bin(n)[2:].replace('0','0'*n),2) # _Chai Wah Wu_, Jan 29 2021

%Y Main diagonal of A340666.

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

%K nonn,look,base

%O 0,3

%A _Alois P. Heinz_, Jan 15 2021