A330524 Lexicographically earliest sequence of positive terms such that for any distinct i and j, a(i) | a(j+1) <> a(j) | a(j+1) (where "|" corresponds to binary concatenation, A163621).

1, 1, 2, 1, 3, 2, 2, 3, 3, 4, 1, 4, 2, 4, 3, 5, 2, 5, 3, 6, 1, 8, 1, 9, 2, 8, 2, 9, 3, 7, 4, 4, 5, 4, 8, 3, 8, 4, 9, 4, 10, 2, 11, 2, 13, 1, 10, 4, 11, 3, 9, 5, 8, 5, 9, 6, 4, 15, 2, 16, 1, 16, 2, 17, 2, 18, 4, 16, 3, 10, 5, 10, 6, 5, 11, 4, 17, 3, 11, 5, 14

Offset: 1

Author

Rémy Sigrist, Dec 17 2019

Keywords

• nonn
• base

Comments

This sequence is a binary variant of A318225.

This sequence has similarities with A088177; here we combine successive terms by concatenation, there by multiplication.

This sequence is necessarily unbounded.

Also, the value 1 appears infinitely many times.

Examples

			The first terms, alongside their binary representation and that of the concatenation of two consecutive terms, are:
  n   a(n)  bin(a(n))  bin(a(n)|a(n+1))
  --  ----  ---------  ----------------
   1     1          1                11
   2     1          1               110
   3     2         10               101
   4     1          1               111
   5     3         11              1110
   6     2         10              1010
   7     2         10              1011
   8     3         11              1111
   9     3         11             11100
  10     4        100              1001
  11     1          1              1100
  12     4        100             10010
		

Links

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

Crossrefs

See A330525 for the concatenation of consecutive terms.

Cf. A088177, A163621, A318225.

Programs

PARI

s=0; v=1; for (n=1, 81, print1 (v", "); for (w=1, oo, if (!bittest(s, k=v*2^#binary(w)+w), s+=2^k; v=w; break)))