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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.
0
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.
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: A076179 A373546 A175213 * A369293 A104492 A331522
KEYWORD
nonn,easy
AUTHOR
Walter Carlini, Jul 07 2021
STATUS
approved