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 A338619 #16 Nov 12 2020 01:16:32 %S A338619 1,2,4,3,8,9,10,5,7,14,11,6,12,13,15,18,17,16,20,19,22,24,23,21,27,25, %T A338619 33,35,28,29,26,30,31,32,34,37,36,38,41,40,42,43,39,45,44,46,47,48,50, %U A338619 49,52,54,53,51,57,55,63,56,59,58,60,61,62,64,65,66,68 %N A338619 Lexicographically earliest sequence of distinct positive terms such that among three consecutive terms there is exactly one pair of terms that are not coprime. %C A338619 In other words, for any n > 0, exactly one of gcd(a(n), a(n+1)), gcd(a(n), a(n+2)), gcd(a(n+1), a(n+2)) is strictly greater than 1. %C A338619 This sequence has connections with the Yellowstone permutation (A098550). %C A338619 Conjecture: this sequence is a permutation of the natural numbers. %H A338619 Rémy Sigrist, <a href="/A338619/b338619.txt">Table of n, a(n) for n = 1..10000</a> %H A338619 Rémy Sigrist, <a href="/A338619/a338619.gp.txt">PARI program for A338619</a> %e A338619 The first terms, alongside associated GCD's, are: %e A338619 n a(n) gcd(a(n),a(n+1)) gcd(a(n),a(n+2)) gcd(a(n+1),a(n+2)) %e A338619 -- ---- ---------------- ---------------- ------------------ %e A338619 1 1 1 1 2 %e A338619 2 2 2 1 1 %e A338619 3 4 1 4 1 %e A338619 4 3 1 3 1 %e A338619 5 8 1 2 1 %e A338619 6 9 1 1 5 %e A338619 7 10 5 1 1 %e A338619 8 5 1 1 7 %e A338619 9 7 7 1 1 %e A338619 10 14 1 2 1 %o A338619 (PARI) See Links section. %Y A338619 See A338618 for a similar sequence. %Y A338619 Cf. A084937, A098550. %K A338619 nonn %O A338619 1,2 %A A338619 _Rémy Sigrist_, Nov 04 2020