A345903 The succession of prime and nonprime 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.

2, 1, 3, 4, 5, 6, 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

Offset: 1

Author

Eric Angelini and Carole Dubois, Jul 02 2021

Keywords

• nonn

Examples

			Here is the succession of primes and nonprimes in the sequence:
2,  1,  3,  4,  5,  6,  8,  7, 10, 11, 12,  9, 13, 16, 14, 18, 15, ...
p   n   p   n   p   n   n   p   n   p   n   n   p   n   n   n   n
The same succession is formed by a(n) + a(n+1):
3,  4,  7,  9, 11, 14, 15, 17, 21, 23, 21, 22, 29, 30, 32, 33, 32, ...
p   n   p   n   p   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. A345966.

Programs

Mathematica

seq[n_] := Module[{s = {2}, 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, Jul 02 2021 *)

Formula

a(n) = A345966(n) for n >= 7. - Pontus von Brömssen, Jul 03 2021