A338524 prime(n) Gray code decoding.

3, 2, 6, 5, 13, 9, 30, 29, 26, 22, 21, 57, 49, 50, 53, 38, 45, 41, 125, 122, 113, 117, 98, 110, 65, 70, 69, 77, 73, 94, 85, 253, 241, 242, 230, 229, 233, 194, 197, 201, 221, 217, 213, 129, 134, 133, 157, 149, 189, 185, 177, 181, 161, 173, 510, 506, 502, 501

Offset

1,1

Links

Table of n, a(n) for n=1..58.

Eric Weisstein's World of Mathematics, Gray code.

Formula

a(n) = A006068(A000040(n)). - Joerg Arndt, Nov 01 2020

Example

f(x) = gray_code_to_natural(x) = A006068(x),
a(1) = f(2) = 3,
a(2) = f(3) = 2,
a(3) = f(5) = 6,
a(4) = f(7) = 5,
a(5) = f(11) = 13.

Mathematica

Array[BitXor @@ Table[Floor[#/2^m], {m, 0, Floor@ Log2[#]}] &@ Prime[#] &, 58] (* Michael De Vlieger, Nov 05 2020 *)

Prog

(Ruby) require 'prime'
values = Prime.first(50).map { |x| x ^= x >> 16; x ^= x >> 8; x ^= x >> 4; x ^= x >> 2; x ^= x >> 1; x }
p values
(Python)
from sympy import prime
def A338524(n):
    k = prime(n)
    m = k>>1
    while m > 0:
        k ^= m
        m >>= 1
    return k # Chai Wah Wu, Jun 29 2022

Crossrefs

Cf. A000040, A006068, A143292 (Gray code of prime(n)).

Sequence in context: A125675 A301501 A072787 * A371906 A293549 A370377

Adjacent sequences: A338521 A338522 A338523 * A338525 A338526 A338527

Keyword

nonn

Author

Simon Strandgaard, Nov 01 2020

Status

approved