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

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

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=n-p-q); if(r>q, r==nextprime(q+2), r==precprime(p-1) && 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: A136020 A356467 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