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A157996
Primes which are sum of 1 and two nonconsecutive primes p1 and p2, p2 - p1 > 2.
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved