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A270753 The least prime q > p for which n = p + q - r for some prime r, where p = A270003(n).

%I A270753 #9 Jun 21 2025 14:46:26
%S A270753 5,3,3,5,5,7,7,11,11,11,11,13,13,17,17,17,17,19,19,23,23,23,23,29,29,
%T A270753 29,29,29,29,31,31,37,37,37,37,37,37,41,41,41,41,43,43,47,47,47,47,53,
%U A270753 53,53,53,53,53,59,59,59,59,59,59,61,61,67,67,67,67,67
%N A270753 The least prime q > p for which n = p + q - r for some prime r, where p = A270003(n).
%H A270753 Clark Kimberling, <a href="/A270753/b270753.txt">Table of n, a(n) for n = 1..10000</a>
%F A270753 Conjecture: a(n) = A066169(n-1) for n>2. - _R. J. Mathar_, Jun 21 2025
%e A270753 n   p   q   r
%e A270753 1   3   5   7
%e A270753 2   2   3   3
%e A270753 3   2   3   2
%e A270753 4   2   5   3
%e A270753 5   2   5   2
%e A270753 6   2   7   3
%e A270753 7   2   7   2
%t A270753 t = Join[{{1, {3, 5, 7}}, {2, {2, 3, 3}}}, Table[If[PrimeQ[n], {n, {2, n, 2}}, p = If[EvenQ[2 + NextPrime[n, 1] - n], 3, 2]; NestWhile[# + 1 &, 1, ! PrimeQ[r = (p + (q = NextPrime[n, #])) - n] &]; {n, {p, q, r}}], {n, 3, 300}]];
%t A270753 Map[#[[2]][[1]] &, t] (* p, A270003 *)
%t A270753 Map[#[[2]][[2]] &, t] (* q, A270753 *)
%t A270753 Map[#[[2]][[3]] &, t] (* r, A271353 *)
%t A270753 (* _Peter J. C. Moses_, Apr 26 2016 *)
%Y A270753 Cf. A000040, A270003, A271353.
%K A270753 nonn,easy
%O A270753 1,1
%A A270753 _Clark Kimberling_, Apr 26 2016