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.

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, 53, 59, 61, 67, 20, 21, 22, 24, 25, 26, 27, 71, 73, 79, 83, 89, 97, 101, 103, 107, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42

Offset: 1

Author

Walter Carlini, Jul 07 2021

Keywords

• nonn
• easy

Comments

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.

Examples

			a(1) = 2, this being a length 1 (1 is initial index) run of primes.
a(2) = 4 & a(3) = 6, 4 and 6 being a length 2 (2 is first prime) run of composites.
a(4) = 3, a(5) = 5, a(6) = 7, and a(7) = 11 being a length 4 (4 is first composite) run of primes.
a(8) = 8, a(9) = 9, and a(10) = 10, being a length 3 (3 is 2nd prime) run of composites.
		

Crossrefs

Cf. A000040 (primes), A002808 (composites), A073846.

Programs

Mathematica

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 *)