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

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, 29, 29, 29, 29, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 43, 43, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 59, 59, 59, 59, 61, 61, 67, 67, 67, 67, 67

Offset: 1

Author

Clark Kimberling, Apr 26 2016

Keywords

• nonn
• easy

Examples

			n   p   q   r
1   3   5   7
2   2   3   3
3   2   3   2
4   2   5   3
5   2   5   2
6   2   7   3
7   2   7   2
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A270003, A271353.

Programs

Mathematica

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}]];
Map[#[[2]][[1]] &, t] (* p, A270003 *)
Map[#[[2]][[2]] &, t] (* q, A270753 *)
Map[#[[2]][[3]] &, t] (* r, A271353 *)
(* Peter J. C. Moses, Apr 26 2016 *)

Formula

Conjecture: a(n) = A066169(n-1) for n>2. - R. J. Mathar, Jun 21 2025