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A084951 Primes in A075893: Primes of the form (p^2+q^2+r^2)/3, where p,q,r are 3 consecutive primes. 9
113, 193, 577, 1913, 2833, 10753, 44617, 48593, 54617, 69193, 74177, 78593, 86729, 102673, 107873, 122273, 156577, 183497, 214993, 228233, 247697, 308809, 334513, 414313, 581177, 602753, 617369, 636353, 691697, 861857, 1408993, 1786097 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

With the exception of 2^2+3^2+5^2=38 and 3^2+5^2+7^2=83 all sums of squares of 3 consecutive primes are divisible by 3 because mod(p^2,3)=1 for all primes p>3.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1)=113 because (7^2+11^2+13^2)/3=(49+121+169)/3=339/3=113 is prime.

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 - Artur Jasinski, Sep 30 2007

PROG

(PARI) v=vector(10000); i=0; p=5; q=7; forprime(r=8, 1e8, if(isprime(t=(p^2+q^2+r^2)/3), v[i++]=t; if(i==#v, return)); p=q; q=r) \\ Charles R Greathouse IV, Feb 14 2011

CROSSREFS

Cf. A075893, A084952, A133529, A133940.

Sequence in context: A152929 A142180 A325084 * A151947 A087703 A056710

Adjacent sequences:  A084948 A084949 A084950 * A084952 A084953 A084954

KEYWORD

easy,nonn

AUTHOR

Hugo Pfoertner, Jun 14 2003

EXTENSIONS

Edited by N. J. A. Sloane, Jun 30 2008 at the suggestion of R. J. Mathar.

STATUS

approved

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Last modified April 25 16:59 EDT 2019. Contains 322461 sequences. (Running on oeis4.)