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A122560 Primes p such that p^2 is a sum of three successive primes, or primes in A076304. 4

%I

%S 7,11,29,31,43,151,157,191,263,311,359,367,563,823,859,881,929,997,

%T 1013,1019,1021,1087,1297,1471,1613,1733,1787,1913,2153,2161,2203,

%U 2293,2411,2473,2543,2549,2557,2579,2689,2731,2971,3209,3253,3299,3779,3881,3923

%N Primes p such that p^2 is a sum of three successive primes, or primes in A076304.

%C A076304(n) are the Numbers n such that n^2 is a sum of three successive primes.

%H Donovan Johnson and Charles R Greathouse IV, <a href="/A122560/b122560.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 from Johnson)

%e A076304(n) begins {7,11,29,31,43,151,157,191,209,217,...}.

%e So a(1) = 7 because A076304(1) = 7 is prime and 7^2 = 49 = 13 + 17 + 19 = p(6) + p(7) + p(8).

%t Select[Table[Sqrt[Sum[Prime[k], {k, n, n + 2}]], {n, 400000}], PrimeQ] (* _Ray Chandler_, Sep 26 2006 *)

%o (PARI) has(n)=my(p=precprime(n\3), q=nextprime(n\3+1), r=n-p-q); if(r>q, r==nextprime(q+2), r==precprime(p-1) && r)

%o list(lim)=my(v=List()); forprime(p=7,lim, if(has(p^2), listput(v,p))); Vec(v) \\ _Charles R Greathouse IV_, Jun 26 2019

%Y Cf. A076304.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Sep 20 2006

%E Extended by _Ray Chandler_, Sep 26 2006

%E Name edited by _Zak Seidov_, May 07 2014

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Last modified January 28 06:00 EST 2021. Contains 340490 sequences. (Running on oeis4.)