A114265 Smallest prime p greater than prime(n) such that 2*prime(n) + p is a prime.

3, 5, 7, 17, 19, 17, 19, 23, 37, 31, 41, 53, 67, 53, 73, 61, 61, 71, 89, 97, 83, 83, 97, 103, 113, 109, 107, 139, 113, 127, 167, 139, 157, 179, 151, 197, 173, 173, 223, 211, 199, 239, 211, 227, 199, 233, 239, 227, 229, 233, 277, 241, 251, 271, 283, 271, 271, 281

Offset

1,1

Comments

Note that p is next prime after prime(n) iff prime(n) is a term in A173971. - Zak Seidov, Feb 11 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

n=1: 2*prime[1]+3=2*2+3=7 is prime, so a(1)=3;
n=2: 2*prime[2]+5=2*3+5=11 is prime, so a(2)=5;
...
n=4: 2*prime[4]+3=2*7+3=17 is prime, so a(4)=17.

Mathematica

Table[p1 = Prime[n1]; n2 = 1; p2 = Prime[n1 + n2]; While[cp = 2*p1 + p2; ! PrimeQ[cp], n2++; p2 = Prime[n1 + n2]]; p2, {n1, 1, 200}]

Prog

(Haskell)
a114265 n = head [p | let (q:qs) = drop (n - 1) a000040_list, p <- qs,
                      a010051 (2 * q + p) == 1]
-- Reinhard Zumkeller, Oct 31 2013
(PARI) a(n)=forprime(p=prime(n)+1, , if(isprime(2*prime(n)+p), return(p)))
vector(100, n, a(n)) \\ Derek Orr, Feb 11 2015

Crossrefs

Cf. A114227, A114230, A073703, A114235, A114262.

Cf. A010051, A000040, A173971.

Sequence in context: A031441 A078150 A276044 * A377939 A258195 A110358

Adjacent sequences: A114262 A114263 A114264 * A114266 A114267 A114268

Keyword

easy,nonn

Author

Lei Zhou, Nov 20 2005

Extensions

Edited definition to conform to OEIS style. - Reinhard Zumkeller, Oct 31 2013

Status

approved