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

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Last modified April 21 01:28 EDT 2021. Contains 343143 sequences. (Running on oeis4.)