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

1,2

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

Links

Table of n, a(n) for n=1..35.

Formula

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

Example

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.

Maple

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

Prog

(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

Crossrefs

Cf. A054429, A059459, A059661, A139803.

Sequence in context: A096780 A332454 A143986 * A259630 A114883 A125091

Adjacent sequences: A059659 A059660 A059661 * A059663 A059664 A059665

Keyword

nonn,more,base

Author

Antti Karttunen, Feb 03 2001

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

Status

approved