A027864 Primes of the form k^2 + (k+1)^2 + (k+2)^2 = 3*(k+1)^2+2.

5, 29, 149, 509, 677, 1877, 3677, 8429, 9749, 11909, 13469, 17789, 22709, 27077, 28229, 45389, 46877, 53069, 70229, 72077, 81677, 100469, 102677, 114077, 128549, 141269, 154589, 180077, 192029, 195077, 207509, 223589, 230189, 261077, 312989, 340709

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• easy

Comments

Same as A257163 without its first term. - Jonathan Sondow, Oct 24 2015

The domain of k is not explicit. If the domain is all integers then the sequence A257163 is produced. In this sequence domain is all nonnegative integers. - Michael Somos, Oct 24 2015

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 247.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A027574, A257163.

Programs

Mathematica

Select[Table[3n^2+6n+5,{n,0,400}],PrimeQ] (* Harvey P. Dale, Oct 22 2016 *)
Select[Table[Total[Range[n,n+2]^2],{n,0,500}],PrimeQ] (* Harvey P. Dale, May 23 2021 *)

PARI

select(isprime, vector(100,n,3*n^2+2)) \\ Charles R Greathouse IV, Apr 17 2015

Python

from sympy import isprime
print(list(filter(isprime, (3*k**2+6*k+5 for k in range(350))))) # Michael S. Branicky, May 29 2021

Extensions

More terms from Claudio Meller, Jun 25 2009