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, 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

Links

Table of n, a(n) for n=1..80.

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

Adjacent sequences: A345963 A345964 A345965 * A345967 A345968 A345969

Keyword

nonn

Author

Eric Angelini and Carole Dubois, Jun 30 2021

Status

approved