A349102 Increase the odd part of n to the next greater odd number.

3, 6, 5, 12, 7, 10, 9, 24, 11, 14, 13, 20, 15, 18, 17, 48, 19, 22, 21, 28, 23, 26, 25, 40, 27, 30, 29, 36, 31, 34, 33, 96, 35, 38, 37, 44, 39, 42, 41, 56, 43, 46, 45, 52, 47, 50, 49, 80, 51, 54, 53, 60, 55, 58, 57, 72, 59, 62, 61, 68, 63, 66, 65, 192, 67, 70, 69

Offset

1,1

Comments

This is +2 at the bit position of the odd part of n, that being the least significant 1-bit.

The least significant run of 1-bits changes from 0111..111 in n to 1000..001 in a(n).

Arrays A054582 and A135764 arrange terms into rows having the same number of trailing 0 bits. a(n) is the term to the right of n, i.e., next in its row.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = n + A171977(n).

a(2*n) = 2*a(n).

a(2*n+1) = 2*n + 3.

Example

n    = 3448 = binary 1101 0111 1 000
a(n) = 3464 = binary 1101 1000 1 000

Mathematica

Array[# + 2^(IntegerExponent[#, 2] + 1) &, 67] (* Michael De Vlieger, Mar 27 2022 *)

Prog

(PARI) a(n) = n + 2<<valuation(n, 2);

Crossrefs

Cf. A000265 (odd part), A171977 (2 at odd part), A285326.

Arrays: A054582, A135764.

Sequence in context: A299209 A007479 A076535 * A285327 A239487 A246979

Adjacent sequences: A349099 A349100 A349101 * A349103 A349104 A349105

Keyword

nonn,easy

Author

Kevin Ryde, Mar 26 2022

Status

approved