A028874 -id:A028874 - cp's OEIS frontend

A028873 Numbers k such that k^2 - 3 is prime.

4, 8, 10, 14, 20, 26, 32, 34, 40, 44, 46, 58, 64, 68, 80, 86, 88, 92, 98, 110, 112, 118, 124, 128, 136, 140, 142, 146, 164, 172, 190, 194, 202, 206, 208, 218, 220, 250, 254, 266, 268, 296, 298, 304, 310, 320, 322, 326, 328, 332, 340, 350, 356, 362, 370, 416, 418

Offset: 1

Patrick De Geest

			8^2 - 3 = 61 is prime, so 8 is in the sequence.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Patrick De Geest, Palindromic Quasipronics of the form n(n+x).
Eric Weisstein's World of Mathematics, Near-Square Prime.

Cf. A028874.

[n: n in [2..10000] |IsPrime(n^2-3)]; // Vincenzo Librandi, Aug 05 2010

Select[Range[2, 500], PrimeQ[#^2 - 3] &] (* Amiram Eldar, Mar 01 2025 *)

is(n)=isprime(n^2-3) \\ Charles R Greathouse IV, Jul 02 2013

a(n) = sqrt(A028874(n) + 3). - Amiram Eldar, Mar 01 2025

A083022 Numbers n such that 4*n^2 - 3 is prime.

Original entry on oeis.org

2, 4, 5, 7, 10, 13, 16, 17, 20, 22, 23, 29, 32, 34, 40, 43, 44, 46, 49, 55, 56, 59, 62, 64, 68, 70, 71, 73, 82, 86, 95, 97, 101, 103, 104, 109, 110, 125, 127, 133, 134, 148, 149, 152, 155, 160, 161, 163, 164, 166, 170, 175, 178, 181, 185, 208, 209, 218, 220

Offset: 1

Hugo Pfoertner, May 31 2003

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A028874.

[n: n in [1..300] | IsPrime(4*n^2 - 3)]; // Vincenzo Librandi, Oct 05 2012

Select[Range[300], PrimeQ[4 #^2 - 3] &] (* Vincenzo Librandi, Oct 05 2012 *)

is(n)=isprime(4*n^2-3) \\ Charles R Greathouse IV, May 22 2017

a(n) = A028873(n)/2.

A302443 Number of primes of the form b^2-3 for b <= 10^n.

Original entry on oeis.org

3, 19, 119, 849, 6663, 54514, 460019, 3982973, 35174007

Offset: 1

Seiichi Manyama, Apr 08 2018

			a(1) = 3 because there are 3 primes of the form b^2-3 for b <= 10 : 13, 61 and 97.

Number of primes of the form b^2+m for b <= 10^n: this sequence (m=-3), A302442 (m=-2), A206709 (m=1), A302434 (m=2), A302435 (m=3).

Cf. A028874.

PARI
```
{a(n) = sum(k=0, 10^n, isprime(k^2-3))}
```

A162860 Numbers k such that k^2+4*k+1 is prime.

Original entry on oeis.org

2, 6, 8, 12, 18, 24, 30, 32, 38, 42, 44, 56, 62, 66, 78, 84, 86, 90, 96, 108, 110, 116, 122, 126, 134, 138, 140, 144, 162, 170, 188, 192, 200, 204, 206, 216, 218, 248, 252, 264, 266, 294, 296, 302, 308, 318, 320, 324, 326, 330, 338, 348, 354, 360, 368, 414, 416

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 14 2009

			a(1) = k = 2 is in the sequence because 2^2+4*2+1=13 = A028874(1) is prime.

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

Cf. A028874.

f[a_]:=a^2+4*a+1; lst={};Do[If[PrimeQ[f[n]],AppendTo[lst,n]],{n,6!}]; lst
Select[Range[500],PrimeQ[#^2+4#+1]&] (* Harvey P. Dale, May 28 2012 *)

a(n) = A028873(n)-2. - R. J. Mathar, Aug 12 2009

cp's OEIS Frontend

A028873 Numbers k such that k^2 - 3 is prime.

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A083022 Numbers n such that 4*n^2 - 3 is prime.

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A302443 Number of primes of the form b^2-3 for b <= 10^n.

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PARI

A162860 Numbers k such that k^2+4*k+1 is prime.

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Mathematica

Formula