A338248 Nonnegative values in A053985, in order of appearance.

0, 1, 4, 5, 2, 3, 16, 17, 14, 15, 20, 21, 18, 19, 8, 9, 6, 7, 12, 13, 10, 11, 64, 65, 62, 63, 68, 69, 66, 67, 56, 57, 54, 55, 60, 61, 58, 59, 80, 81, 78, 79, 84, 85, 82, 83, 72, 73, 70, 71, 76, 77, 74, 75, 32, 33, 30, 31, 36, 37, 34, 35, 24, 25, 22, 23, 28, 29

Offset: 0

Author

Rémy Sigrist, Oct 18 2020

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers (the offset has been set to 0 so as to get a permutation).

There are only two fixed points: a(0) = 0 and a(1) = 1.

Examples

			A053985 = 0, 1, -2, -1, 4, 5, 2, 3, -8, -7, -10, -9, -4, -3, -6, -5, 16, 17, ...
We keep:  0, 1,         4, 5, 2, 3,                                  16, 17, ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..5461
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

See A338245 for a similar sequence.

Cf. A053738, A053985, A338249.

Programs

PARI

A053985(n) = fromdigits(binary(n), -2)
print (select(v -> v>=0, apply(A053985, [0..109])))

Formula

a(0) = 0.

a(n) = A053985(A053738(n)) for any n > 0.