A305410 - OEIS

A305410

a(1) = 1, and for any n > 0, a(2*n) = a(n) + k(n) and a(2*n+1) = a(n) + 2 * k(n) where k(n) is the least positive integer not leading to a duplicate term.

1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 14, 9, 13, 11, 15, 16, 24, 17, 22, 18, 26, 21, 28, 19, 29, 20, 27, 23, 35, 30, 45, 25, 34, 31, 38, 32, 47, 33, 44, 36, 54, 37, 48, 39, 57, 40, 52, 41, 63, 42, 55, 43, 66, 46, 65, 49, 75, 51, 67, 50, 70, 53, 61, 56, 87, 58, 82

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

OFFSET

1,2

COMMENTS

Apparently, every positive integer appears in the sequence.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of (n, a(n)) for n = 1..10000000

FORMULA

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

EXAMPLE

The first terms, alongside k(n) and associate children, are:

n a(n) k(n) a(2*n) a(2*n+1)

-- ---- ---- ------ --------

1 1 1 2 3

2 2 2 4 6

3 3 2 5 7

4 4 4 8 12

5 6 4 10 14

6 5 4 9 13

7 7 4 11 15

8 8 8 16 24

9 12 5 17 22

10 10 8 18 26

PROG

(PARI) lista(nn) = my (a=[1], s=2^a[1]); for (n=1, ceil(nn/2), for (k=1, oo, if (!bittest(s, a[n]+k) && !bittest(s, a[n]+2*k), a=concat(a, [a[n]+k

, a[n]+2*k]); s+=2^(a[n]+k) + 2^(a[n]+2*k); break))); a[1..nn]

CROSSREFS

This sequence is a variant of A322510.

Sequence in context: A306869 A139708 A333776 * A059893 A331274 A269365

Adjacent sequences: A305407 A305408 A305409 * A305411 A305412 A305413

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Dec 16 2018

EXTENSIONS

Name corrected by Rémy Sigrist, Apr 26 2020

STATUS

approved