A157996 Primes which are sum of 1 and two nonconsecutive primes p1 and p2, p2 - p1 > 2.

11, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283

Offset

1,1

Comments

Conjecture: for n > 1, a(n) = prime(n+5). - Charles R Greathouse IV, Mar 12 2012

A185154(n) is the smallest prime q, such that A049084(q) + 1 < A049084(a(n) - q - 1). - Reinhard Zumkeller, Mar 12 2012

Links

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

Example

11=3+7+1, 17=5+11+1, 19=5+13+1, ...

Mathematica

lst={}; Do[p0=Prime[n]; Do[px=Prime[n+k]; If[PrimeQ[a=p0+px+1], AppendTo[lst, a]], {k, 2, 2*5!}], {n, 6!}]; Take[Union[lst], 222]

Prog

(Haskell)
a157996 n = a157996_list !! (n-1)
a157996_list = map (+ 1) $ filter f a006093_list where
   f x = g $ takeWhile (< x) a065091_list where
     g []  = False
     g [_] = False
     g (p:ps@(_:qs)) = (x - p) `elem` qs || g ps
-- Reinhard Zumkeller, Mar 12 2012
(PARI) is(n)=if(!isprime(n), return(0)); my(p=3, q=5); forprime(r=7, n-4, if(isprime(n-1-r) && n-1-r <= p, return(1)); p=q; q=r); 0 \\ Charles R Greathouse IV, Nov 05 2015

Crossrefs

Cf. A000040, A076805, A005385, A092738, A118071, A157995, A065091, A006093.

Sequence in context: A226630 A061751 A063449 * A050713 A217063 A038966

Adjacent sequences: A157993 A157994 A157995 * A157997 A157998 A157999

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 11 2009

Status

approved