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A305410 a(1) = 0, 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. 3
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: A139706 A306869 A139708 * A059893 A331274 A269365

Adjacent sequences:  A305407 A305408 A305409 * A305411 A305412 A305413

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Dec 16 2018

STATUS

approved

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Last modified February 20 22:47 EST 2020. Contains 332086 sequences. (Running on oeis4.)