A344682 a(0) = 0, and for any n > 0, a(n) = A022290(A059893(A003754(n+1))).

0, 1, 2, 3, 5, 4, 6, 7, 10, 9, 8, 11, 15, 13, 18, 12, 17, 16, 14, 19, 20, 28, 26, 23, 31, 25, 22, 30, 21, 29, 27, 24, 32, 41, 36, 49, 34, 47, 44, 39, 52, 33, 46, 43, 38, 51, 42, 37, 50, 35, 48, 45, 40, 53, 54, 75, 70, 62, 83, 68, 60, 81, 57, 78, 73, 65, 86, 67

Offset: 0

Author

Rémy Sigrist, Jun 08 2021

Keywords

• nonn
• look
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

The construction of this sequence is similar to that of A343150; we start with a representation of a number n as a sum of distinct positive Fibonacci numbers, through some binary encoding, and we reverse some of the bits in a bijective way to obtain a(n).

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10944
• Rémy Sigrist, PARI program for A344682
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A003754, A059893, A022290, A343150.

Programs

Maple

# after renaming a(n) to A059893(n) in A059893...
A344682 := proc(n)
    if n = 0 then
        0;
    else
        A022290(A059893(A003754(n+1))) ;
    end if;
end proc:
seq(A344682(n),n=0..70) ; # R. J. Mathar, Jul 29 2021

PARI

See Links section.