A053641 - OEIS

A053641

Rotate n one binary digit to the right, drop leading zeros, then rotate one binary digit to the left.

1, 1, 3, 1, 5, 3, 7, 1, 9, 3, 11, 5, 13, 7, 15, 1, 17, 3, 19, 5, 21, 7, 23, 9, 25, 11, 27, 13, 29, 15, 31, 1, 33, 3, 35, 5, 37, 7, 39, 9, 41, 11, 43, 13, 45, 15, 47, 17, 49, 19, 51, 21, 53, 23, 55, 25, 57, 27, 59, 29, 61, 31, 63, 1

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

OFFSET

1,3

LINKS

Jason Yuen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A006257(A038572(n)).

a(n) = n if n odd, n - 2^k + 1 if n even and 2^k <= n < 2^(k+1).

EXAMPLE

a(60) = 29 because starting with 111100 the right rotation produces 011110, written as 11110 (i.e., 30) and the left rotation produces 11101 (i.e., 29).

MATHEMATICA

rtt[f_, n_] := FromDigits[f[IntegerDigits[n, 2]], 2];

Array[rtt[RotateLeft, rtt[RotateRight, #]]&, 100] (* Paolo Xausa, Jan 16 2024 *)

PROG

(PARI) a(n) = if(bitand(n, 1), n, n+1 - 1<<logint(n, 2)); \\ Kevin Ryde, Jan 13 2024

CROSSREFS

Cf. A006257, A038572.

Cf. A053642 (left then right).

Sequence in context: A116528 A357111 A081431 * A161825 A099551 A211206

Adjacent sequences: A053638 A053639 A053640 * A053642 A053643 A053644

KEYWORD

nonn,base,easy

AUTHOR

Henry Bottomley, Mar 22 2000

STATUS

approved