A258269 Primes of the form p^3 + q^2 + r, where p, q, r are consecutive primes.

59, 5297, 7417, 81769, 152419, 714479, 1237037, 3330907, 25248317, 64648901, 84801217, 90728159, 286628773, 530133671, 554065817, 823543381, 1028270917, 1096980919, 1299792317, 1321357391, 1417523659, 1574410169, 1648622903, 1997248987, 2084078057, 2556384373

Offset: 1

Author

K. D. Bajpai, May 25 2015

Keywords

• nonn

Examples

			a(1) = 59 is prime of the form 3^3 + 5^2 + 7.
a(2) = 5297 is prime of the form 17^3 + 19^2 + 23.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A034962, A133529, A133530.

Programs

Magma

[k: p in PrimesUpTo (3000) | IsPrime(k) where k is (p^3 + NextPrime(p)^2 + NextPrime(NextPrime(p)))];

Maple

A258269:= n-> (ithprime(n)^3+ithprime(n+1)^2+ithprime(n+2)): select(isprime, [seq((A258269(n), n=1..5000))]);

Mathematica

Select[Table[p = Prime[n]; q = NextPrime[p]; r = NextPrime[q]; p^3 + q^2 + r, {n, 5000}], PrimeQ]

PARI

forprime(p=1, 5000, q=nextprime(p+1); r=nextprime(q+1);  k=(p^3 + q^2 + r); if(isprime(k), print1(k,", ")))