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 A338618 #17 Jun 13 2021 03:24:09 %S A338618 1,2,4,3,6,5,8,10,7,12,9,11,15,18,13,14,16,17,20,22,19,24,21,23,27,30, %T A338618 25,26,28,29,32,34,31,36,33,35,39,40,38,37,42,44,41,46,48,43,45,50,47, %U A338618 52,54,49,51,56,57,58,60,53,55,65,59,70,62,61,64,66,63 %N A338618 Lexicographically earliest sequence of distinct positive integers such that three consecutive terms are never pairwise coprime. %C A338618 In other words, for any n > 0, at least 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 A338618 This sequence has connections with the Yellowstone permutation (A098550). %C A338618 Conjecture: this sequence is a permutation of the natural numbers. %H A338618 Rémy Sigrist, <a href="/A338618/b338618.txt">Table of n, a(n) for n = 1..10000</a> %H A338618 Rémy Sigrist, <a href="/A338618/a338618.gp.txt">PARI program for A338618</a> %e A338618 The first terms, alongside associated GCD's, are: %e A338618 n a(n) gcd(a(n),a(n+1)) gcd(a(n),a(n+2)) gcd(a(n+1),a(n+2)) %e A338618 -- ---- ---------------- ---------------- ------------------ %e A338618 1 1 1 1 2 %e A338618 2 2 2 1 1 %e A338618 3 4 1 2 3 %e A338618 4 3 3 1 1 %e A338618 5 6 1 2 1 %e A338618 6 5 1 5 2 %e A338618 7 8 2 1 1 %e A338618 8 10 1 2 1 %e A338618 9 7 1 1 3 %e A338618 10 12 3 1 1 %o A338618 (PARI) See Links section. %Y A338618 See A338619 for a similar sequence. %Y A338618 Cf. A084937, A098550. %K A338618 nonn %O A338618 1,2 %A A338618 _Rémy Sigrist_, Nov 04 2020