A145342 a(n) = (A145341(n) + 1)/2.

1, 2, 3, 4, 5, 7, 6, 8, 9, 13, 11, 15, 10, 14, 12, 16, 17, 25, 21, 29, 19, 27, 23, 31, 18, 26, 22, 30, 20, 28, 24, 32, 33, 49, 41, 57, 37, 53, 45, 61, 35, 51, 43, 59, 39, 55, 47, 63, 34, 50, 42, 58, 38, 54, 46, 62, 36, 52, 44, 60, 40, 56, 48, 64, 65, 97, 81, 113, 73, 105, 89

Offset: 1

Author

Leroy Quet, Oct 08 2008

Keywords

• base
• nonn

Comments

This sequence is a permutation of the positive integers. It is its own inverse permutation.

Fixed points of the permutation are the terms of A044051. - Ivan Neretin, Oct 31 2015

From Yosu Yurramendi, Feb 04 2019: (Start)

If the terms (n > 0) are written as an array (left-aligned fashion) with rows of length 2^m, m = 0,1,2,3,...

1;

2, 3;

4, 5, 7, 6;

8, 9, 13, 11, 15, 10, 14, 12;

16, 17, 25, 21, 29, 19, 27, 23, 31, 18, 26, 22, 30, 20, 28, 24;

32, 33, 49, 41, 57, 37, 53, 45, 61, 35, 51, 43, 59, 39, 55, 47, 63, 34, ...

then the following relationship can be observed:

a(1) = 1, a(2) = 2, a(3) = 3,

for m > 0, a(2^(m+1)) = 2*a(2^m), a(2^m + 1) = a(2^m) + 1, a(2^(m+1)+ 2^m) = 2*a(2^(m+1)) - 1, for 0 < k < 2^m, a(2^(m+1)+ k) = 2*a(2^m + k) - 1, a(2^(m+1)+ 2^m + k) = a(2^(m+1) + k) + 1

(End)

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A044051, A145341.

Programs

Mathematica

Table[(FromDigits[Reverse[IntegerDigits[2n-1, 2]], 2] +1)/2, {n, 71}] (* Ivan Neretin, Oct 31 2015 *)

PARI

a(n) = (1+fromdigits(Vecrev(binary(2*n-1)), 2))/2; \\ Michel Marcus, Feb 04 2019

R

nmax <- 10^3 # by choice
b <- vector()
for (o in seq(1,nmax,2)){
  w <- which(as.numeric(intToBits(o))==1)
  b <- c(b, sum(2^(max(w)-w)))
}
a <- (b+1)/2
a[1:71]
# Yosu Yurramendi, Feb 04 2019

Extensions

More terms from R. J. Mathar and Ray Chandler, Oct 10 2008