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A158351
Primes p0 such that p0+p1+p2-+2 are primes; p0,p1,p2 are three consecutive primes.
1
3, 251, 523, 1063, 4007, 4373, 4423, 7517, 11801, 11833, 11927, 12491, 12757, 12967, 15817, 15907, 16381, 16481, 16763, 16987, 17851, 21341, 21937, 22343, 22441, 22877, 23327, 25849, 26591, 26993, 27061, 31153, 31321, 31583, 33773, 35159
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
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
Sequence in context: A349644 A124875 A226986 * A025418 A075901 A028918
KEYWORD
nonn
AUTHOR
STATUS
approved