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

Author

Rémy Sigrist, Jul 24 2020

Keywords

• nonn
• base

Comments

This sequence is inspired by Ulam sequence (A002858).

Examples

			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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A336527

Crossrefs

Cf. A002858, A336528 (decimal variant).

Programs

PARI

See Links section.