A114235 Largest prime p < prime(n) such that 2*prime(n) + p is a prime.

3, 5, 7, 11, 13, 5, 13, 13, 17, 29, 31, 41, 43, 43, 31, 59, 59, 37, 53, 71, 73, 79, 89, 79, 101, 103, 89, 67, 113, 127, 127, 131, 103, 137, 149, 137, 157, 163, 163, 179, 181, 191, 193, 179, 197, 197, 223, 173, 211, 223, 227, 241, 229, 193, 223, 269, 269, 277, 263

Offset: 3

Author

Lei Zhou, Nov 20 2005

Keywords

• easy
• nonn

Examples

			n=3: 2*prime(3)+3=2*5+3=13 is prime, so a(3)=3;
n=4: 2*prime(4)+5=2*7+5=19 is prime, so a(4)=5;
...
n=8: 2*prime(8)+17=2*19+17=55 is not prime
2*prime(8)+13=2*19+13=51 is not prime
...
2*prime(8)+5=2*19+5=43 is prime, so a(8)=5;
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A114227, A114230, A073703.

Cf. A000040, A010051.

Programs

Haskell

a114235 n = head [p | let q = a000040 n,
                      p <- reverse $ takeWhile (< q) a000040_list,
                      a010051 (2 * q + p) == 1]
-- Reinhard Zumkeller, Oct 29 2013

Mathematica

Table[p1 = Prime[n1]; n2 = 1; p2 = Prime[n1 - n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; If[n2 >= n1, Print[n1]]; p2 = Prime[n1 - n2]]; p2, {n1, 3, 202}]

Extensions

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