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

1,2

Comments

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

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

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

Formula

A144016(a(n)) >= n.

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A056744, A144016, A344183.

Sequence in context: A377950 A266005 A056744 * A164859 A332868 A261467

Adjacent sequences: A344181 A344182 A344183 * A344185 A344186 A344187

Keyword

nonn,base

Author

Rémy Sigrist, May 11 2021

Status

approved