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

Author

Rémy Sigrist, Feb 20 2021

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, Perl program for A341798

Crossrefs

Cf. A006995, A030101, A030190, A030304.

Programs

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

Formula

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