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A345966
The succession of nonprime and prime terms is kept when you consider the sequence formed by the successive sums a(n) + a(n+1). This is the lexicographically earliest sequence of distinct positive terms with this property.
1
1, 3, 2, 5, 6, 4, 8, 7, 10, 11, 12, 9, 13, 16, 14, 18, 15, 17, 20, 19, 22, 23, 24, 21, 25, 26, 28, 27, 29, 30, 32, 31, 36, 33, 35, 34, 38, 37, 42, 39, 41, 48, 40, 44, 43, 46, 45, 47, 50, 49, 51, 53, 54, 52, 56, 55, 57, 58, 59, 68, 60, 61, 66, 62, 63, 65, 64, 69, 67, 70, 71, 78, 72, 73, 76, 74, 79, 84, 75, 77
OFFSET
1,2
COMMENTS
Here is the succession of nonprimes and primes in the sequence:
1, 3, 2, 5, 6, 4, 8, 7, 10, 11, 12, 9, 13, 16, 14, 18, 15,
n p p p n n n p n p n n p n n n n
The same succession is formed by a(n) + a(n+1):
4, 5, 7, 11, 10, 12, 15, 17, 21, 23, 21, 22, 29, 30, 32, 33, 32
n p p p n n n p n p n n p n n n n
MATHEMATICA
seq[n_] := Module[{s = {1}, q, k}, Do[q = PrimeQ[s[[-1]]]; k = 1; While[!FreeQ[s, k] || PrimeQ[s[[-1]] + k] != q, k++]; AppendTo[s, k], {n}]; s]; seq[100] (* Amiram Eldar, Jun 30 2021 *)
CROSSREFS
Cf. A094044.
Sequence in context: A303776 A230599 A245445 * A066181 A195115 A194060
KEYWORD
nonn
AUTHOR
Eric Angelini and Carole Dubois, Jun 30 2021
STATUS
approved