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A377738 a(n) is the least m > n such that the Zeckendorf representations of m and n have the same number of terms.

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%I A377738 #10 Nov 20 2024 14:11:55
%S A377738 2,3,5,6,8,7,9,13,10,11,14,17,21,15,16,18,19,22,20,25,34,23,24,26,27,
%T A377738 29,28,30,35,31,32,38,46,55,36,37,39,40,42,41,43,47,44,45,48,51,56,49,
%U A377738 50,52,53,59,54,67,89,57,58,60,61,63,62,64,68,65,66,69,72
%N A377738 a(n) is the least m > n such that the Zeckendorf representations of m and n have the same number of terms.
%C A377738 A permutation of the numbers missing from A027941.
%C A377738 To compute a(n):
%C A377738 - in the Zeckendorf representation of n,
%C A377738 - locate the rightmost term A000045(k) such that A000045(k+2) is not a term,
%C A377738 - replace A000045(k) by A000045(k+1),
%C A377738 - replace the c terms < A000045(k) by A027941(c).
%H A377738 Rémy Sigrist, <a href="/A377738/b377738.txt">Table of n, a(n) for n = 1..10000</a>
%H A377738 Rémy Sigrist, <a href="/A377738/a377738.gp.txt">PARI program</a>
%H A377738 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F A377738 a(A000045(k)) = A000045(k+1) for any k >= 2.
%e A377738 The first terms, alongside their Zeckendorf representations, are:
%e A377738   n   a(n)  A014417(n)  A014417(a(n))
%e A377738   --  ----  ----------  -------------
%e A377738    1     2           1             10
%e A377738    2     3          10            100
%e A377738    3     5         100           1000
%e A377738    4     6         101           1001
%e A377738    5     8        1000          10000
%e A377738    6     7        1001           1010
%e A377738    7     9        1010          10001
%e A377738    8    13       10000         100000
%e A377738    9    10       10001          10010
%e A377738   10    11       10010          10100
%e A377738   11    14       10100         100001
%e A377738   12    17       10101         100101
%e A377738   13    21      100000        1000000
%e A377738   14    15      100001         100010
%o A377738 (PARI) \\ See Links section.
%Y A377738 Cf. A000045, A003714, A007895, A014417, A027941, A057168, A228915.
%K A377738 nonn,base
%O A377738 1,1
%A A377738 _Rémy Sigrist_, Nov 05 2024