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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.

%I A336527 #10 Jul 27 2020 01:30:14
%S A336527 1,2,5,6,11,14,21,23,26,27,29,30,47,62,85,86,87,90,95,106,107,111,117,
%T A336527 122,125,126,171,174,183,186,187,191,219,234,237,238,239,246,251,254,
%U A336527 341,347,349,351,363,383,426,431,442,447,470,471,474,479,491,495,501
%N 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.
%C A336527 This sequence is inspired by Ulam sequence (A002858).
%H A336527 Rémy Sigrist, <a href="/A336527/b336527.txt">Table of n, a(n) for n = 1..10000</a>
%H A336527 Rémy Sigrist, <a href="/A336527/a336527.gp.txt">PARI program for A336527</a>
%e A336527 The first terms, alongside the binary representations of the natural numbers with the corresponding concatenations of distinct smaller terms, are:
%e A336527   n  a(n)  k   bin(k)  concatenations
%e A336527   -  ----  --  ------  --------------
%e A336527   1     1   1       1
%e A336527   2     2   2      10
%e A336527             3      11
%e A336527             4     100
%e A336527   3     5   5     101  10|1
%e A336527   4     6   6     110  1|10
%e A336527             7     111
%e A336527             8    1000
%e A336527             9    1001
%e A336527            10    1010
%e A336527   5    11  11    1011  101|1
%e A336527            12    1100
%e A336527            13    1101  1|101, 110|1
%e A336527   6    14  14    1110  1|110
%o A336527 (PARI) See Links section.
%Y A336527 Cf. A002858, A336528 (decimal variant).
%K A336527 nonn,base
%O A336527 1,2
%A A336527 _Rémy Sigrist_, Jul 24 2020