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

1,3

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.

Links

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

Example

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

Prog

(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)))

Crossrefs

See A330525 for the concatenation of consecutive terms.

Cf. A088177, A163621, A318225.

Sequence in context: A205784 A066272 A237130 * A336037 A058773 A122805

Adjacent sequences: A330521 A330522 A330523 * A330525 A330526 A330527

Keyword

nonn,base

Author

Rémy Sigrist, Dec 17 2019

Status

approved