A345903 - OEIS

%I #24 Jul 04 2021 16:05:23

%S 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,

%T 28,27,29,30,32,31,36,33,35,34,38,37,42,39,41,48,40,44,43,46,45,47,50,

%U 49,51,53,54,52,56,55,57,58,59,68,60,61,66,62,63,65,64,69,67,70

%N 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.

%F a(n) = A345966(n) for n >= 7. - _Pontus von Brömssen_, Jul 03 2021

%e Here is the succession of primes and nonprimes in the sequence:

%e 2,  1,  3,  4,  5,  6,  8,  7, 10, 11, 12,  9, 13, 16, 14, 18, 15, ...

%e p   n   p   n   p   n   n   p   n   p   n   n   p   n   n   n   n

%e The same succession is formed by a(n) + a(n+1):

%e 3,  4,  7,  9, 11, 14, 15, 17, 21, 23, 21, 22, 29, 30, 32, 33, 32, ...

%e p   n   p   n   p   n   n   p   n   p   n   n   p   n   n   n   n

%t 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 *)

%Y Cf. A345966.

%K nonn

%O 1,1

%A _Eric Angelini_ and _Carole Dubois_, Jul 02 2021