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

1,1

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.

Links

Table of n, a(n) for n=1..56.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A077179 A076179 A175213 * A369293 A104492 A331522

Adjacent sequences: A346147 A346148 A346149 * A346151 A346152 A346153

Keyword

nonn,easy

Author

Walter Carlini, Jul 07 2021

Status

approved