A217497 Primes of the form 2*n^2 + 54*n + 25.

421, 673, 2473, 4561, 5821, 9601, 12301, 14281, 19861, 30661, 32173, 33721, 61261, 67741, 84121, 94273, 107773, 110581, 122173, 134341, 170773, 203821, 207673, 223441, 227473, 265381, 274201, 287701, 344941, 365173, 391273, 396601, 418273, 423781, 469141

Offset: 1

Author

Vincenzo Librandi, Oct 09 2012

Keywords

• nonn
• easy

Comments

Conjecture: 2^a(n)-1 is not prime; in other words, these primes are included in A054723.

2*a(n) + 679 is a square. - Vincenzo Librandi, Apr 10 2015

Equivalently, primes of the form 36*n^2 + 36*n + 9. - Charles R Greathouse IV, Jul 24 2024

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3000

Crossrefs

Subsequence of A002144.

Cf. A054723, A176549, A217494.

Programs

Magma

[a: n in [1..500] | IsPrime(a) where a is 2*n^2+54*n+25];

Mathematica

Select[Table[2 n^2 + 54 n + 25, {n, 500}], PrimeQ]

PARI

list(lim)=my(v=List()); for(n=2,(sqrtint(lim\1*2+679)-27)\6, my(p=18*n^2 + 162*n + 25); if(isprime(p), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jul 24 2024

Formula

a(n) >> n^2 log n. - Charles R Greathouse IV, Jul 24 2024