A133940 Numbers n such that (prime(n)^2 + prime(n+1)^2 + prime(n+2)^2)/3 is prime (A084951).

4, 5, 8, 13, 15, 26, 46, 47, 50, 55, 57, 59, 61, 65, 66, 69, 77, 82, 89, 91, 94, 101, 105, 116, 134, 136, 137, 138, 144, 157, 194, 216, 219, 221, 224, 225, 229, 230, 234, 249, 257, 261, 263, 271, 272, 275, 306, 316, 319, 323

Offset: 1

Author

Artur Jasinski, Sep 30 2007

Keywords

• nonn

Comments

With the exception of the first two terms, all numbers in A133529 are divisible by 3.

Examples

			a(1)=4 because (prime(4)^2 + prime(5)^2 + prime(6)^2)/3 = 113 is prime.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A133529, A084951.

Programs

Maple

select(n -> isprime((ithprime(n)^2 + ithprime(n+1)^2 + ithprime(n+2)^2)/3), [$3 .. 1000]); # Robert Israel, Apr 21 2015

Mathematica

b = {}; a = 2; Do[k = (Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a)/3; If[PrimeQ[k], AppendTo[b, n]], {n, 1, 200}]; b

PARI

is(n)=my(p=prime(n),q=nextprime(p+1),r=nextprime(q+1)); n>3 && isprime((p^2+q^2+r^2)/3) \\ Charles R Greathouse IV, Apr 21 2015

Extensions

Corrected and edited by Zak Seidov, Apr 21 2015