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A361645 a(n) is the least k such that n appears in the k-th row of triangle A361644.

%I A361645 #14 Mar 21 2023 15:04:20
%S A361645 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 A361645 20,18,18,17,16,32,33,34,34,36,37,37,36,40,41,42,42,42,42,41,40,40,41,
%U A361645 42,42,42,42,41,40,36,37,37,36,34,34,33,32,64,65,66,66
%N A361645 a(n) is the least k such that n appears in the k-th row of triangle A361644.
%C A361645 All terms are fibbinary numbers (A003714).
%C A361645 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 A361645 See A361676 for the greatest k's.
%H A361645 Rémy Sigrist, <a href="/A361645/b361645.txt">Table of n, a(n) for n = 0..8191</a>
%H A361645 Rémy Sigrist, <a href="/A361645/a361645.gp.txt">PARI program</a>
%H A361645 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A361645 a(n) <= n with equality iff n is a fibbinary number (A003714).
%F A361645 a(n) <= A361676(n) with equality iff n belongs to A000975.
%e A361645 The first terms, in decimal and in binary, are:
%e A361645   n   a(n)  bin(n)  bin(a(n))
%e A361645   --  ----  ------  ---------
%e A361645    0     0       0          0
%e A361645    1     1       1          1
%e A361645    2     2      10         10
%e A361645    3     2      11         10
%e A361645    4     4     100        100
%e A361645    5     5     101        101
%e A361645    6     5     110        101
%e A361645    7     4     111        100
%e A361645    8     8    1000       1000
%e A361645    9     9    1001       1001
%e A361645   10    10    1010       1010
%e A361645   11    10    1011       1010
%e A361645   12    10    1100       1010
%e A361645   13    10    1101       1010
%e A361645   14     9    1110       1001
%e A361645   15     8    1111       1000
%o A361645 (PARI) See Links section.
%Y A361645 Cf. A000975, A003714, A101211, A361645, A361676.
%K A361645 nonn,base
%O A361645 0,3
%A A361645 _Rémy Sigrist_, Mar 19 2023