cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A370631 Lexicographically earliest sequence of distinct positive integers such that the Zeckendorf expansions of two consecutive terms have at least one common term.

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%I A370631 #11 May 04 2024 09:25:56
%S A370631 1,4,3,11,8,9,6,5,7,2,10,12,14,13,15,16,17,18,19,20,23,21,22,24,25,26,
%T A370631 27,28,29,30,31,32,33,35,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A370631 50,51,52,53,54,57,55,56,58,59,60,61,62,63,64,65,66,67
%N A370631 Lexicographically earliest sequence of distinct positive integers such that the Zeckendorf expansions of two consecutive terms have at least one common term.
%C A370631 This sequence is a permutation of the positive integers with inverse A370632:
%C A370631 - for k >= 7, the values whose Zeckendorf expansions have largest term A000045(k) appear in a single run of consecutive values; the first value being A000045(k) + 1 or 2, the second value being A000045(k), the remaining values appearing in ascending order.
%H A370631 Rémy Sigrist, <a href="/A370631/a370631.gp.txt">PARI program</a>
%H A370631 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%H A370631 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A370631 A000120(A003714(a(n)), A003714(a(n+1))) > 0.
%e A370631 The first terms, alongside the Zeckendorf expansion in binary of a(n), are:
%e A370631   n   a(n)  z(a(n))
%e A370631   --  ----  -------
%e A370631    1     1        1
%e A370631    2     4      101
%e A370631    3     3      100
%e A370631    4    11    10100
%e A370631    5     8    10000
%e A370631    6     9    10001
%e A370631    7     6     1001
%e A370631    8     5     1000
%e A370631    9     7     1010
%e A370631   10     2       10
%e A370631   11    10    10010
%e A370631   12    12    10101
%o A370631 (PARI) \\ See Links section.
%Y A370631 Cf. A000045, A000120, A003714, A115510, A370630, A370632 (inverse).
%K A370631 nonn,base
%O A370631 1,2
%A A370631 _Rémy Sigrist_, May 01 2024