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

Author

Rémy Sigrist, Dec 16 2018

Keywords

• nonn
• look
• nice

Comments

Apparently every positive integer appears in the sequence.

Examples

			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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of (n, a(n)) for n = 1..10000000

Crossrefs

This sequence is a variant of A305410.

Programs

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]

Formula

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