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.
%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