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

1,1

Comments

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

Links

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

Example

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

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

Prog

(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

Crossrefs

Cf. A133529, A084951.

Sequence in context: A242274 A297419 A230549 * A174398 A341420 A030978

Adjacent sequences: A133937 A133938 A133939 * A133941 A133942 A133943

Keyword

nonn

Author

Artur Jasinski, Sep 30 2007

Extensions

Corrected and edited by Zak Seidov, Apr 21 2015

Status

approved