A336527 a(1) = 1; a(2) = 2; for n > 2, a(n) is the least number > a(n-1) whose binary representation is uniquely the concatenation of the binary representations of two distinct earlier terms.

1, 2, 5, 6, 11, 14, 21, 23, 26, 27, 29, 30, 47, 62, 85, 86, 87, 90, 95, 106, 107, 111, 117, 122, 125, 126, 171, 174, 183, 186, 187, 191, 219, 234, 237, 238, 239, 246, 251, 254, 341, 347, 349, 351, 363, 383, 426, 431, 442, 447, 470, 471, 474, 479, 491, 495, 501

Offset

1,2

Comments

This sequence is inspired by Ulam sequence (A002858).

Links

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

Rémy Sigrist, PARI program for A336527

Example

The first terms, alongside the binary representations of the natural numbers with the corresponding concatenations of distinct smaller terms, are:
  n  a(n)  k   bin(k)  concatenations
  -  ----  --  ------  --------------
  1     1   1       1
  2     2   2      10
            3      11
            4     100
  3     5   5     101  10|1
  4     6   6     110  1|10
            7     111
            8    1000
            9    1001
           10    1010
  5    11  11    1011  101|1
           12    1100
           13    1101  1|101, 110|1
  6    14  14    1110  1|110

Prog

(PARI) See Links section.

Crossrefs

Cf. A002858, A336528 (decimal variant).

Sequence in context: A015613 A135013 A239447 * A293398 A180323 A103035

Adjacent sequences: A336524 A336525 A336526 * A336528 A336529 A336530

Keyword

nonn,base

Author

Rémy Sigrist, Jul 24 2020

Status

approved