OFFSET
1,1
COMMENTS
sum of three consecutive primes = arithmetical mean of two primes. 3+5+7=15-+2 (13,17)primes, 251+257+263-+2 (769,773)primes, ...
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
MATHEMATICA
lst={}; Do[p0=Prime[n]; p1=Prime[n+1]; p2=Prime[n+2]; a=p0+p1+p2; If[PrimeQ[a-2]&&PrimeQ[a+2], AppendTo[lst, p0]], {n, 2*7!}]; lst
Select[Partition[Prime[Range[4000]], 3, 1], AllTrue[Total[#]+{2, -2}, PrimeQ]&][[;; , 1]] (* Harvey P. Dale, Apr 23 2024 *)
PROG
(PARI) is(n)=my(p=nextprime(n+1), q=nextprime(p+1)); isprime(n) && isprime(n+p+q-2) && isprime(n+p+q+2) \\ Charles R Greathouse IV, Jan 29 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Mar 16 2009
STATUS
approved