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
Keywords
Examples
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).
Links
- Donovan Johnson and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 from Johnson)
Crossrefs
Cf. A076304.
Programs
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Mathematica
Select[Table[Sqrt[Sum[Prime[k], {k, n, n + 2}]], {n, 400000}], PrimeQ] (* Ray Chandler, Sep 26 2006 *) -
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
Extensions
Extended by Ray Chandler, Sep 26 2006
Name edited by Zak Seidov, May 07 2014
Comments