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 A126638 #19 Jun 01 2022 01:53:21
%S A126638 4,9,25,26,27,35,38,39,49,50,51,77,80,81,91,92,93,95,98,99,115,116,
%T A126638 117,119,121,122,123,125,128,129,133,134,135,143,146,147,155,158,159,
%U A126638 161,164,165,169,172,175,177,178,185,187,188,189,205,206,207,209,212,213
%N A126638 a(n) is larger than a(n-1), not prime and coprime to a(n-1) and a(n-2).
%H A126638 Harvey P. Dale, <a href="/A126638/b126638.txt">Table of n, a(n) for n = 1..1000</a>
%e A126638 a(7) = 38 because it is the next composite number larger than 35 (a(6)) that shares no factors in common with 35 and 27 (a(5)).
%p A126638 with(numtheory); i:=4; j:=9; k:=10; while(k < 100) do while(order(k, i) = FAIL or order(k,j) = FAIL or isprime(k)) do k:=k+1; end do; print(k); i:= j; j:=k; k:=k+1; end do;
%t A126638 f[l_List] := Block[{k = l[[ -1]] + 1},While[PrimeQ[k] || GCD[k, l[[ -1]]*l[[ -2]]] > 1, k++ ];Append[l, k]];Nest[f, {4, 9}, 56] (* _Ray Chandler_, Feb 14 2007 *)
%t A126638 nxt[{a_,b_}]:=Module[{k=b+1},While[PrimeQ[k]||!CoprimeQ[a,k] || !CoprimeQ[ b,k],k++];{b,k}]; NestList[nxt,{4,9},60][[All,1]] (* _Harvey P. Dale_, Aug 31 2021 *)
%Y A126638 Cf. A051884.
%K A126638 nonn
%O A126638 1,1
%A A126638 _Ben Paul Thurston_, Feb 08 2007
%E A126638 Extended by _Ray Chandler_, Feb 14 2007