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A133940 Numbers n such that (prime(n)^2 + prime(n+1)^2 + prime(n+2)^2)/3 is prime (A084951). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 21 19:59 EDT 2021. Contains 345365 sequences. (Running on oeis4.)