A341798 a(n) is the starting position of the first occurrence of the binary reversal of n in the binary Champernowne word (A030190).

0, 1, 0, 1, 7, 2, 0, 4, 19, 6, 8, 1, 23, 2, 3, 15, 51, 18, 21, 5, 7, 26, 0, 11, 56, 22, 8, 1, 66, 2, 14, 46, 131, 50, 54, 17, 20, 63, 58, 4, 143, 6, 27, 25, 23, 77, 10, 41, 137, 55, 21, 34, 7, 28, 0, 11, 149, 65, 8, 1, 173, 13, 45, 125, 323, 130, 135, 49, 53

Offset

0,5

Comments

This sequence is a variant of A030304.

When considering the binary reversal of a positive number, the trailing zeros in that number turn into leading zeros in its binary reversal; we keep those leading zeros.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, Perl program for A341798

Formula

a(n) = A030304(n) iff n is a binary palindrome (A006995).

Example

For n = 4:
- the binary reversal of 4 is "001",
- the binary Champernowne word begins "0110111001011...",
- the first occurrence of "001" in this word starts at position 7,
- so a(4) = 7.

Prog

(Perl) See Links section.
(Python)
from itertools import count, islice
def agen():
    k, chap = 0, "0"
    for n in count(0):
        target = bin(n)[2:][::-1]
        while chap.find(target) == -1: k += 1; chap += bin(k)[2:]
        yield chap.find(target)
print(list(islice(agen(), 70))) # Michael S. Branicky, Oct 06 2022

Crossrefs

Cf. A006995, A030101, A030190, A030304.

Sequence in context: A248363 A220674 A102771 * A232812 A245740 A318922

Adjacent sequences: A341795 A341796 A341797 * A341799 A341800 A341801

Keyword

nonn,base

Author

Rémy Sigrist, Feb 20 2021

Status

approved