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a(n) is the least k such that the binary expansion of n is a self-infiltration of that of k.
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%I #17 Mar 15 2023 16:27:48

%S 0,1,2,1,2,5,2,3,4,5,2,5,2,5,6,3,4,9,10,5,4,5,10,11,4,5,6,5,6,13,6,7,

%T 8,9,18,9,4,9,10,11,4,9,10,5,10,5,22,11,4,9,10,5,10,5,6,11,12,13,6,13,

%U 6,13,14,7,8,17,18,9,18,9,18,19,8,9,10,19,10,21

%N a(n) is the least k such that the binary expansion of n is a self-infiltration of that of k.

%C See A361398 for the definition of an infiltration (a self-infiltration is an infiltration a of word with itself).

%C a(n) is the index of the first row of A361401 containing n.

%H Rémy Sigrist, <a href="/A361399/b361399.txt">Table of n, a(n) for n = 0..8192</a>

%H Rémy Sigrist, <a href="/A361399/a361399.png">Colored log-log scatterplot of the first 2^20 terms</a> (the color is function of A070939(a(n)) - A070939(n))

%H Rémy Sigrist, <a href="/A361399/a361399.gp.txt">PARI program</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) <= n.

%F a(A020330(n)) = n.

%o (PARI) See Links section.

%Y Cf. A020330, A070939, A361398, A361401.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Mar 10 2023