

A122560


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


4



7, 11, 29, 31, 43, 151, 157, 191, 263, 311, 359, 367, 563, 823, 859, 881, 929, 997, 1013, 1019, 1021, 1087, 1297, 1471, 1613, 1733, 1787, 1913, 2153, 2161, 2203, 2293, 2411, 2473, 2543, 2549, 2557, 2579, 2689, 2731, 2971, 3209, 3253, 3299, 3779, 3881, 3923
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

Donovan Johnson and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 from Johnson)


EXAMPLE

A076304(n) begins {7,11,29,31,43,151,157,191,209,217,...}.
So a(1) = 7 because A076304(1) = 7 is prime and 7^2 = 49 = 13 + 17 + 19 = p(6) + p(7) + p(8).


MATHEMATICA

Select[Table[Sqrt[Sum[Prime[k], {k, n, n + 2}]], {n, 400000}], PrimeQ] (* Ray Chandler, Sep 26 2006 *)


PROG

(PARI) has(n)=my(p=precprime(n\3), q=nextprime(n\3+1), r=npq); if(r>q, r==nextprime(q+2), r==precprime(p1) && r)
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


CROSSREFS

Cf. A076304.
Sequence in context: A067006 A136020 A076304 * A136338 A193867 A110572
Adjacent sequences: A122557 A122558 A122559 * A122561 A122562 A122563


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Sep 20 2006


EXTENSIONS

Extended by Ray Chandler, Sep 26 2006
Name edited by Zak Seidov, May 07 2014


STATUS

approved



