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 A354803 #12 Jun 13 2022 08:45:10 %S A354803 1,1,2,3,1,4,3,5,1,7,2,5,4,7,3,8,1,9,2,11,1,13,2,15,4,9,5,7,6,11,3,13, %T A354803 4,11,5,8,7,9,8,11,7,10,9,11,10,13,5,16,1,17,2,19,1,23,2,25,1,27,2,29, %U A354803 1,31,2,37,1,32,3,16,7,12,11,13,6,17,3,19,4,17,5,19,6,23,3,25,4,23 %N A354803 a(1) = 1; for n > 1, a(n) is the smallest positive number that is coprime to a(n-1) and the product a(n) * a(n-1) is distinct from all previous products a(i) * a(i-1), i=2..n-1. %C A354803 This sequences uses similar a similar rule to A088177 but here all neighboring terms are coprime. In the first 1000000 terms the only fixed point is the first term while the smallest number not to have appeared is 2054. The sequence is conjectured to be a permutation of the positive integers. %C A354803 See A354804 for the products of all pairs of terms. %H A354803 Scott R. Shannon, <a href="/A354803/a354803.png">Image of the first 500000 terms</a>. %e A354803 a(5) = 1 as a(4) = 3 and 1 is the smallest positive number that is coprime to 3 and whose product with 3, 1 * 3 = 3, has not previously appeared. %Y A354803 Cf. A354804, A354749, A354759, A354753, A354754, A088177, A317024. %K A354803 nonn,look %O A354803 1,3 %A A354803 _Scott R. Shannon_, Jun 07 2022