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 A346150 #22 Oct 28 2021 03:58:48
%S A346150 2,4,6,3,5,7,11,8,9,10,13,17,19,23,29,31,12,14,15,16,18,37,41,43,47,
%T A346150 53,59,61,67,20,21,22,24,25,26,27,71,73,79,83,89,97,101,103,107,28,30,
%U A346150 32,33,34,35,36,38,39,40,42
%N A346150 Alternating runs of primes and composites, with the runs of primes being of composite length and the runs of composites being of prime length.
%C A346150 In other words, use sequence A073846 to list alternating runs of primes and composites, with the number of elements in each run given by successive terms in A073846 - with each even-indexed term of A073846 (being itself prime) denoting the length of each run of composites and each odd-indexed term of A073846 (being itself composite) denoting the length of each run of primes.
%e A346150 a(1) = 2, this being a length 1 (1 is initial index) run of primes.
%e A346150 a(2) = 4 & a(3) = 6, 4 and 6 being a length 2 (2 is first prime) run of composites.
%e A346150 a(4) = 3, a(5) = 5, a(6) = 7, and a(7) = 11 being a length 4 (4 is first composite) run of primes.
%e A346150 a(8) = 8, a(9) = 9, and a(10) = 10, being a length 3 (3 is 2nd prime) run of composites.
%t A346150 m=10;c1=Select[Range@m,!PrimeQ@#&];p1=Prime@Range@Total@c1;p2=Prime@Range@m;c2=Select[Range[2,2Total@p2],!PrimeQ@#&][[;;Total@p2]];t1=TakeList[p1,c1];t2=TakeList[c2,p2];min=Min[Length/@{t1,t2}];Flatten@Riffle[t1[[;;min]],t2[[;;min]]] (* _Giorgos Kalogeropoulos_, Jul 30 2021 *)
%Y A346150 Cf. A000040 (primes), A002808 (composites), A073846.
%K A346150 nonn,easy
%O A346150 1,1
%A A346150 _Walter Carlini_, Jul 07 2021