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

Author

Eric Angelini and Carole Dubois, Jun 30 2021

Keywords

• nonn

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

• Dominic McCarty, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A094044, A345903.

Programs

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 *)