A304971 a(1) = 0, and for any n > 0, a(2*n) = a(n) + k(n) and a(2*n+1) = a(n) + 3 * k(n) where k(n) is the least positive integer not leading to a duplicate term in the sequence.

1, 2, 4, 3, 5, 6, 10, 7, 15, 8, 14, 11, 21, 12, 16, 9, 13, 18, 24, 17, 35, 19, 29, 20, 38, 23, 27, 22, 42, 25, 43, 26, 60, 28, 58, 30, 54, 31, 45, 32, 62, 37, 41, 33, 61, 34, 44, 36, 68, 47, 65, 39, 71, 40, 66, 46, 94, 49, 63, 50, 100, 51, 67, 48, 92, 64, 72

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

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         4
   2     2     1       3         5
   3     4     2       6        10
   4     3     4       7        15
   5     5     3       8        14
   6     6     5      11        21
   7    10     2      12        16
   8     7     2       9        13
   9    15     3      18        24
  10     8     9      17        35

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]+3*k), a=concat(a, [a[n]+k
, a[n]+3*k]); s+=2^(a[n]+k) + 2^(a[n]+3*k); break))); a[1..nn]

Crossrefs

This sequence is a variant of A305410.

Sequence in context: A338254 A132949 A275899 * A338252 A086434 A086433

Adjacent sequences: A304968 A304969 A304970 * A304972 A304973 A304974

Keyword

nonn,look,nice

Author

Rémy Sigrist, Dec 16 2018

Status

approved