A145341 Convert 2n-1 to binary. Reverse its digits. Convert back to decimal to get a(n).

1, 3, 5, 7, 9, 13, 11, 15, 17, 25, 21, 29, 19, 27, 23, 31, 33, 49, 41, 57, 37, 53, 45, 61, 35, 51, 43, 59, 39, 55, 47, 63, 65, 97, 81, 113, 73, 105, 89, 121, 69, 101, 85, 117, 77, 109, 93, 125, 67, 99, 83, 115, 75, 107, 91, 123, 71, 103, 87, 119, 79, 111, 95, 127, 129, 193

Offset

1,2

Comments

This sequence is a permutation of the odd positive integers.

From Yosu Yurramendi, Feb 05 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,

3, 5,

7, 9, 13, 11,

15, 17, 25, 21, 29, 19, 27, 23,

31, 33, 49, 41, 57, 37, 53, 45, 61, 35, 51, 43, 59, 39, 55, 47,

63, 65, 97, 81, 113, 73, 105, 89, 121, 69, 101, 85, 117, 77, 109, 93, 125, ...

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

for m > 0, 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) + 2.

This relationship is enough to reproduce the sequence.

If the terms (n > 0) are written as an array (right-aligned fashion):

1,

3, 5,

7, 9, 13, 11,

15, 17, 25, 21, 29, 19, 27, 23,

31, 33, 49, 41, 57, 37, 53, 45, 61, 35, 51, 43, 59, 39, 55, 47,

... 93, 125, 67, 99, 83, 115, 75, 107, 91, 123, 71, 103, 87, 119, 79, 111, 95,

...

for m >= 0, a(2^(m+1)+2^m) = 4*a(2^m) + 1.

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

(End)

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to binary expansion of n

Formula

a(n) = A030101(2n-1).

a(n) = A145342(n)*2 - 1.

Mathematica

Table[FromDigits[Reverse[IntegerDigits[2*n - 1, 2]], 2], {n, 1, 100}] (* Stefan Steinerberger, Oct 11 2008 *)

Prog

(R)
  nmax <- 10^3 # by choice
  a <- vector()
  for (o in seq(1, nmax, 2)){
    w <- which(as.numeric(intToBits(o))==1)
    a <- c(a, sum(2^(max(w)-w)))
}
a[1:66]
# Yosu Yurramendi, Feb 04 2019
(PARI) a(n) = fromdigits(Vecrev(binary(2*n-1)), 2); \\ Michel Marcus, Feb 04 2019

Crossrefs

Cf. A030101, A145342.

Sequence in context: A362133 A100432 A261033 * A121388 A161700 A245212

Adjacent sequences: A145338 A145339 A145340 * A145342 A145343 A145344

Keyword

base,nonn

Author

Leroy Quet, Oct 08 2008

Extensions

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

Status

approved