A344184 Lexicographically earliest sequence of positive integers such that for any n > 0, the binary expansion of a(n) contains the binary expansion of k for k = 1..n and the binary expansion of a(n+1) is obtained by replacing a possibly empty substring of the binary expansion of a(n) by the binary expansion of n+1.

1, 2, 6, 12, 44, 44, 92, 184, 1208, 1336, 5304, 5304, 10680, 10680, 21368, 42736, 567024, 673520, 5383920, 5383920, 21535472, 172283632, 172283632, 172283632, 344774384, 344774384, 344774384, 344774384, 689559280, 689559280, 1379118576, 2758237152, 71477713888

Offset: 1

Author

Rémy Sigrist, May 11 2021

Keywords

• nonn
• base

Comments

This sequence is a variant of A056744, easier to compute.

This sequence is not weakly increasing; a(109) < a(108).

Examples

			The first terms, alongside their binary expansion, are:
  n   a(n)   bin(n)  bin(a(n))
  --  -----  ------  ---------------
   1      1       1                1
   2      2      10               10
   3      6      11              110
   4     12     100             1100
   5     44     101           101100
   6     44     110           101100
   7     92     111          1011100
   8    184    1000         10111000
   9   1208    1001      10010111000
  10   1336    1010      10100111000
  11   5304    1011    1010010111000
  12   5304    1100    1010010111000
  13  10680    1101   10100110111000
  14  10680    1110   10100110111000
  15  21368    1111  101001101111000
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..1024
• Rémy Sigrist, Binary plot of the first 1024 terms
• Rémy Sigrist, PARI program for A344184

Crossrefs

Cf. A056744, A144016, A344183.

Programs

PARI

See Links section.

Formula

A144016(a(n)) >= n.