This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345903 #29 Mar 24 2025 06:03:28
%S A345903 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 A345903 28,27,29,30,32,31,36,33,35,34,38,37,42,39,41,48,40,44,43,46,45,47,50,
%U A345903 49,51,53,54,52,56,55,57,58,59,68,60,61,66,62,63,65,64,69,67,70
%N 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.
%H A345903 Dominic McCarty, <a href="/A345903/b345903.txt">Table of n, a(n) for n = 1..10000</a>
%F A345903 a(n) = A345966(n) for n >= 7. - _Pontus von Brömssen_, Jul 03 2021
%e A345903 Here is the succession of primes and nonprimes in the sequence:
%e A345903 2, 1, 3, 4, 5, 6, 8, 7, 10, 11, 12, 9, 13, 16, 14, 18, 15, ...
%e A345903 p n p n p n n p n p n n p n n n n
%e A345903 The same succession is formed by a(n) + a(n+1):
%e A345903 3, 4, 7, 9, 11, 14, 15, 17, 21, 23, 21, 22, 29, 30, 32, 33, 32, ...
%e A345903 p n p n p n n p n p n n p n n n n
%t A345903 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 A345903 Cf. A345966.
%K A345903 nonn
%O A345903 1,1
%A A345903 _Eric Angelini_ and _Carole Dubois_, Jul 02 2021