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%I #14 Mar 21 2023 15:04:20
%S 0,1,2,2,4,5,5,4,8,9,10,10,10,10,9,8,16,17,18,18,20,21,21,20,20,21,21,
%T 20,18,18,17,16,32,33,34,34,36,37,37,36,40,41,42,42,42,42,41,40,40,41,
%U 42,42,42,42,41,40,36,37,37,36,34,34,33,32,64,65,66,66
%N a(n) is the least k such that n appears in the k-th row of triangle A361644.
%C All terms are fibbinary numbers (A003714).
%C To compute a(n): consider the run lengths in the binary expansion of n (i.e. the n-th row of A101211) and replace from left to right each value v > 1 at odd index with (1, v-1); at the end, there remain the run lengths in the binary expansion of a(n).
%C See A361676 for the greatest k's.
%H Rémy Sigrist, <a href="/A361645/b361645.txt">Table of n, a(n) for n = 0..8191</a>
%H Rémy Sigrist, <a href="/A361645/a361645.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 with equality iff n is a fibbinary number (A003714).
%F a(n) <= A361676(n) with equality iff n belongs to A000975.
%e The first terms, in decimal and in binary, are:
%e n a(n) bin(n) bin(a(n))
%e -- ---- ------ ---------
%e 0 0 0 0
%e 1 1 1 1
%e 2 2 10 10
%e 3 2 11 10
%e 4 4 100 100
%e 5 5 101 101
%e 6 5 110 101
%e 7 4 111 100
%e 8 8 1000 1000
%e 9 9 1001 1001
%e 10 10 1010 1010
%e 11 10 1011 1010
%e 12 10 1100 1010
%e 13 10 1101 1010
%e 14 9 1110 1001
%e 15 8 1111 1000
%o (PARI) See Links section.
%Y Cf. A000975, A003714, A101211, A361645, A361676.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Mar 19 2023
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