A036571 Binary packing of Connell sequence (shifted once right).

0, 1, 3, 11, 27, 91, 347, 859, 2907, 11099, 43867, 109403, 371547, 1420123, 5614427, 22391643, 55946075, 190163803, 727034715, 2874518363, 11464452955, 45824191323, 114543668059, 389421575003

Offset: 0

Author

Antti Karttunen

Keywords

• nonn

Comments

Binary representation of n has 1's at positions specified by Connell sequence (A001614).

Examples

			347=101011011 in binary, with 1's at positions 1,2,4,5,7,9.
		

Crossrefs

Cf. A001614, A048721, A048722.

Programs

Python

from itertools import count, islice
from math import isqrt
def A036571_gen(): # generator of terms
    c = 0
    for n in count(1):
        yield c
        c += 1<<(m:=n<<1)-(k:=isqrt(m))-int((m<<2)>(k<<2)*(k+1)+1)-1
A036571_list = list(islice(A036571_gen(),25)) # Chai Wah Wu, Jul 26 2022

Formula

a(0)=0, a(n) = a(n-1) + 2^((2*n - floor((1/2)*(1 + sqrt(8*n - 7)))) - 1).