%I #17 Nov 18 2022 03:39:44

%S 1,2,3,4,5,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,14,14,14,14,14,14,14,

%T 14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,45,45,45,45,

%U 45,45,45,45,45,45,45,45,45,45,45,45,45,45,45,45,45,45

%N a(n) = smallest missing number in A357082(k) for k = 0..n.

%H Michael De Vlieger, <a href="/A357149/b357149.txt">Table of n, a(n) for n = 0..16384</a>

%H Michael De Vlieger, <a href="/A357149/a357149.png">Plot of a(n)</a>, n = 1..2^10 in gold, with A357082(n) = b(n) in black, records in b(n) in red, local minima in b(n) in blue.

%H Rémy Sigrist, <a href="/A357149/a357149.gp.txt">PARI program</a>

%t nn = 2^10; c[_] = False; j = a[0] = 0; u = 1; w = "0"; Do[k = u; While[Or[c[k], StringContainsQ[w, Set[v, IntegerString[j + k, 2]]]], k++]; Set[{a[n], c[k], b[n]}, {k, True, u}]; Set[{j, w}, {k, w <> IntegerString[k, 2]}]; If[k == u, While[c[u], u++]], {n, nn}]; Array[b, nn] (* _Michael De Vlieger_, Sep 15 2022 *)

%o (PARI) See Links section.

%Y Cf. A357082.

%K nonn

%O 0,2

%A _Michael De Vlieger_, Sep 15 2022