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

0,3

Comments

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

Links

Table of n, a(n) for n=0..23.

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A001614, A048721, A048722.

Sequence in context: A289842 A077776 A113836 * A003060 A136983 A210611

Adjacent sequences: A036568 A036569 A036570 * A036572 A036573 A036574

Keyword

nonn

Author

Antti Karttunen

Status

approved