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 A358277 #15 Jan 16 2023 09:10:46
%S A358277 1,2,3,4,5,6,7,8,11,9,10,13,12,17,14,15,19,16,23,18,25,29,20,21,31,22,
%T A358277 27,35,26,33,37,24,41,28,43,30,47,32,53,34,39,49,38,45,59,36,61,40,67,
%U A358277 42,71,44,65,51,46,55,57,52,73,48,79,50,77,69,58,83,54,85,89,56,97,60,101,62,63,95
%N A358277 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that a(n) is coprime to the previous Omega(a(n-1)) terms.
%C A358277 Unlike A356850 all the terms are concentrated along three straight lines. In the first 100000 terms there are ten fixed points, 1, 2, 3, ..., 27, 57, and it is likely no more exist. The sequence is conjectured to be a permutation of the positive integers.
%H A358277 Michael De Vlieger, <a href="/A358277/b358277.txt">Table of n, a(n) for n = 1..16384</a>
%H A358277 Michael De Vlieger, <a href="/A358277/a358277.png">Log log scatterplot of a(n)</a> n = 1..2^10, with records in red, local minima in blue, highlighting primes in green and other prime powers in gold, showing numbers that are neither squarefree nor prime powers in magenta.
%H A358277 Michael De Vlieger, <a href="/A358277/a358277_1.png">Scalar scatterplot of a(n)</a>, n = 1..2^12, showing primes in red, composite prime powers in gold, composite squarefree numbers in green, products of composite prime powers in magenta, and other numbers in blue.
%H A358277 Michael De Vlieger, <a href="/A358277/a358277_2.png">Log-log scatterplot of a(n)</a>, n = 1..2^10 using a color function showing Omega(a(n-1)).
%e A358277 a(4) = 4 as a(3) = 3 and Omega(3) = A001222(3) = 1, and 4 is coprime to the previous one term, namely a(3) = 3.
%e A358277 a(9) = 11 as a(8) = 8 and Omega(8) = A001222(8) = 3, and 11 is coprime to the previous three terms, namely 8, 7, 6.
%t A358277 nn = 90; c[_] = False; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; u = 3; j = 2; Do[k = u; m = Times @@ Array[a[n - #] &, PrimeOmega[j]]; While[Nand[! c[k], CoprimeQ[k, m]], k++]; Set[{a[n], c[k], j}, {k, True, k}]; If[k == u, While[c[u], u++]], {n, 3, nn}]; Array[a, nn] (* _Michael De Vlieger_, Nov 20 2022 *)
%Y A358277 Cf. A356850, A356903, A001222, A356851, A093714, A336957, A000040.
%K A358277 nonn
%O A358277 1,2
%A A358277 _Scott R. Shannon_, Nov 08 2022