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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

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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