A114230 Largest prime p < prime(n) such that prime(n) + 2 * p is a prime.

2, 3, 5, 3, 5, 13, 17, 19, 19, 29, 23, 31, 29, 31, 43, 19, 59, 53, 61, 59, 59, 79, 67, 83, 61, 89, 103, 101, 109, 113, 109, 97, 131, 109, 149, 137, 149, 127, 163, 139, 149, 109, 149, 163, 197, 191, 197, 223, 227, 229, 211, 239, 241, 241, 223, 241, 269, 233, 271, 269

Offset: 2

Author

Lei Zhou, Nov 18 2005

Keywords

• easy
• nonn

Examples

			prime(2)=3, 3+2*2=7 is prime, so a(2)=2;
prime(3)=5, 5+2*3=11 is prime, so a(3)=3;
...
prime(11)=31, 31+2*29=89 is prime, so a(11)=29.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A114227.

Cf. A000040, A010051.

Programs

Haskell

a114230 n = head [p | let q = a000040 n,
                      p <- reverse $ takeWhile (< q) a000040_list,
                      a010051 (q + 2 * p) == 1]
-- Reinhard Zumkeller, Oct 29 2013

Mathematica

Table[p1 = Prime[n1]; n2 = n1 - 1; p2 = Prime[n2]; While[cp = p1 + 2*p2; ! PrimeQ[cp], n2--; If[n2 == 0, Print[n1]]; p2 = Prime[n2]]; p2, {n1, 2, 201}]
lp[n_]:=Module[{p=NextPrime[n,-1]},While[!PrimeQ[n+2p],p=NextPrime[p,-1]];p]; Table[lp[p],{p,Prime[Range[2,70]]}] (* Harvey P. Dale, Jan 17 2022 *)

Extensions

Edited definition to conform to OEIS style. - Reinhard Zumkeller, Oct 29 2013