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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). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 9 03:57 EDT 2020. Contains 336319 sequences. (Running on oeis4.)