A337909 - OEIS

(Translated by https://www.hiragana.jp/)
A337909 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A337909

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

1

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This sequence is a permutation of the positive integers.

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

LINKS

Table of n, a(n) for n=1..65.

Index entries for sequences that are permutations of the natural numbers

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)

EXAMPLE

(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)...

MATHEMATICA

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

PROG

(PARI) a(n) = if(n--, 3<<logint(n, 2) - n, 1); \\ Kevin Ryde, Sep 29 2020

CROSSREFS

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

Sequence in context: A255833 A166133 A237739 * A358523 A365930 A111699

Adjacent sequences: A337906 A337907 A337908 * A337910 A337911 A337912

KEYWORD

nonn

AUTHOR

Lorenzo Sauras Altuzarra, Sep 29 2020

STATUS

approved