A059662 Positions of the flipped bits (here they are always set from 0 to 1) in the sequence A059661.

0, 2, 4, 3, 12, 5, 14, 27, 8, 25, 30, 31, 36, 13, 18, 131, 60, 133, 458, 247, 1040, 21, 618, 283, 300, 209, 6282, 19107, 11792, 3401, 30214, 1211, 3044, 15989, 30194

Offset: 1

Author

Antti Karttunen, Feb 03 2001

Keywords

• nonn
• more
• base

Comments

Question: If A059661 could be extended infinitely, would all the natural numbers > 1 eventually appear here once?

a(31) > 27000. - Michael S. Branicky, Oct 02 2022

Examples

			Starting from A059661(1) = 2, flip (set) bit 0, gives A059661(2) = 3 (= 2+2^0), set bit 2, gives A059661(3) = 7 (3+2^2), set bit 4, gives A059661(4) = 23 (7+2^4), etc.
		

Crossrefs

Cf. A054429, A059459, A059661, A139803.

Programs

Maple

map(floor_log_2,map(abs,DIFF(A059661))); # For floor_log_2, which essentially computes log[2](x) here, see A054429

Python

from sympy import isprime
from itertools import islice
def agen():
    an, bit, p = 2, 1, 0
    while True:
        while an&bit or not isprime(an+bit): bit <<= 1; p += 1
        yield p
        an, bit, p = an+bit, 1, 0
print(list(islice(agen(), 26))) # Michael S. Branicky, Oct 01 2022

Formula

2^a(n) = A059661(n+1) - A059661(n). - Pontus von Brömssen, Jan 08 2023

Extensions

a(21)-a(27) from Sean A. Irvine, Oct 01 2022

a(28)-a(30) from Michael S. Branicky, Oct 02 2022

a(31)-a(35) from Michael S. Branicky, May 29 2023