A337909 Distinct terms of A080079 in the order in which they appear.

1, 2, 4, 3, 8, 7, 6, 5, 16, 15, 14, 13, 12, 11, 10, 9, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 128

Offset: 1

Author

Lorenzo Sauras Altuzarra, Sep 29 2020

Keywords

• nonn

Comments

This sequence is a permutation of the positive integers.

The cardinality of {2^k, ..., (2^k - 0^k)/2 + 1} is A011782(k).

Examples

			(2^0, ..., (2^0 - 0^0)/2 + 1) = (1),
(2^1, ..., (2^1 - 0^1)/2 + 1) = (2),
(2^2, ..., (2^2 - 0^2)/2 + 1) = (4, 3),
(2^3, ..., (2^3 - 0^3)/2 + 1) = (8, 7, 6, 5)...
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A004761, A011782, A053644, A054429, A080079, A280510.

Programs

Mathematica

{1}~Join~Array[3*2^(IntegerLength[# - 1, 2] - 1) - # + 1 &, 64, 2] (* Michael De Vlieger, Oct 05 2020 *)

PARI

a(n) = if(n--, 3<Kevin Ryde, Sep 29 2020

Formula

a(1) = 1 and a(n) = A080079(n - 1 + 2^floor(log_2(n - 1))) if n > 1.

a(n) = A080079(A004761(n+1)).

From Kevin Ryde, Sep 29 2020: (Start)

a(n) = 3*A053644(n-1) - (n-1), if n > 1.

a(n) = A054429(n-1) + 1, if n > 1.

a(n) = A280510(n) - n + 1, if n > 1. (End)