A158351 Primes p0 such that p0+p1+p2-+2 are primes; p0,p1,p2 are three consecutive primes.

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

Author

Vladimir Joseph Stephan Orlovsky, Mar 16 2009

Keywords

• nonn

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

Crossrefs

Cf. A099349, A158350.

Programs

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 *)

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