A090696 -id:A090696 - cp's OEIS frontend

A091271 Numbers k such that 4*k^2-11 is a prime.

2, 4, 5, 9, 10, 14, 16, 19, 21, 24, 26, 31, 35, 39, 40, 45, 59, 60, 65, 74, 79, 80, 86, 91, 100, 105, 109, 114, 115, 116, 119, 124, 126, 129, 130, 131, 135, 136, 145, 149, 150, 151, 159, 170, 171, 175, 179, 180, 185, 186, 189, 194, 199, 205, 206, 210, 219, 221

Offset: 1

Ray Chandler, Dec 27 2003

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

A091272 gives primes, A091273 gives prime index.

Filtered([2..230],n->IsPrime(4*n^2-11)); # Muniru A Asiru, Jul 10 2018

select(t -> isprime(4*t^2-11), [$2..1000]); # Robert Israel, Jul 10 2018

is(n) = ispseudoprime(4*n^2-11) \\ Felix Fröhlich, Jul 10 2018

a(n) = A090696(n)/2.

Offset changed by Robert Israel, Jul 10 2018

A091272 Primes of the form n^2 - 11.

Original entry on oeis.org

5, 53, 89, 313, 389, 773, 1013, 1433, 1753, 2293, 2693, 3833, 4889, 6073, 6389, 8089, 13913, 14389, 16889, 21893, 24953, 25589, 29573, 33113, 39989, 44089, 47513, 51973, 52889, 53813, 56633, 61493, 63493, 66553, 67589, 68633, 72889, 73973

Offset: 1

Ray Chandler, Dec 27 2003

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Primes arising in A090696 and A091271, A091273 gives prime index.

[a: n in [4..600] | IsPrime(a) where a is n^2-11]; // Vincenzo Librandi, Dec 01 2011

lst={};Do[s=n^2;If[PrimeQ[p=s-11], AppendTo[lst, p]], {n, 7!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)
Select[Range[4,1000]^2-11,PrimeQ] (* Vincenzo Librandi, Dec 01 2011 *)

A091273 Indices of primes of the form k^2 - 11.

Original entry on oeis.org

3, 16, 24, 65, 77, 137, 170, 227, 273, 341, 392, 532, 654, 792, 833, 1017, 1645, 1686, 1948, 2456, 2757, 2818, 3210, 3550, 4203, 4589, 4898, 5317, 5397, 5482, 5743, 6186, 6364, 6636, 6735, 6822, 7205, 7300, 8198, 8598, 8713, 8820, 9683, 10920, 11040, 11521, 11997

Offset: 1

Ray Chandler, Dec 27 2003

nonn

A091272 indexed by A000040.

Cf. A090696, A091271, A091272.

Select[Range[12000],IntegerQ[Sqrt[Prime[#]+11]]&]  (* Harvey P. Dale, Jan 16 2011 *)

a(n)=j such that A000040(j)=A091272(n).

Offset changed to 1 by Jinyuan Wang, Aug 02 2021

A296507 Numbers m such that m^2 - 13 is a prime.

Original entry on oeis.org

4, 6, 12, 18, 24, 30, 36, 54, 72, 84, 90, 96, 102, 114, 120, 138, 168, 186, 198, 204, 210, 216, 228, 240, 276, 294, 318, 330, 354, 360, 372, 378, 402, 414, 438, 444, 456, 480, 498, 504, 588, 600, 612, 618, 630, 636, 666, 678, 690, 714, 720, 726, 732, 738, 762

Offset: 1

Zak Seidov, Dec 13 2017

nonn

All terms except 4 are divisible by 6. - Robert Israel, Dec 13 2017

Daniel Starodubtsev, Table of n, a(n) for n = 1..5000

Cf. A028870, A028873, A028876, A028882, A090696.

select(n -> isprime(n^2-13), 2*[$2..10^4]); # Robert Israel, Dec 13 2017

Reap[m=4;Do[If[PrimeQ[m^2-13],Sow[m]];m=m+2,{1000}]][[2,1]]
Select[Range[800],PrimeQ[#^2-13]&] (* Harvey P. Dale, Mar 06 2023 *)

isok(n) = isprime(n^2-13); \\ Michel Marcus, Dec 14 2017

A186815 Numbers n such that n^2-10 is a prime.

Original entry on oeis.org

9, 21, 27, 39, 51, 69, 81, 87, 99, 117, 129, 147, 153, 171, 177, 183, 207, 219, 249, 261, 309, 333, 351, 363, 387, 393, 399, 429, 441, 447, 459, 471, 477, 483, 519, 537, 561, 597, 609, 621, 633, 639, 651, 663, 687, 711, 717, 723, 741, 753, 777, 807, 849

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 27 2011

			9^2-10=71 prime.

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

Cf. A090696, A114273.

[n: n in [1..1000] | IsPrime(n^2-10)]; // Vincenzo Librandi, Jul 10 2016

Mathematica
```
Select[Range[4,1200],PrimeQ[#^2-10]&]
```

A309726 Numbers k such that k^2 - 12 is prime.

Original entry on oeis.org

5, 7, 11, 13, 17, 19, 25, 29, 35, 41, 49, 53, 59, 61, 79, 85, 91, 95, 97, 103, 107, 113, 119, 121, 137, 139, 145, 149, 163, 169, 173, 179, 181, 185, 191, 205, 209, 227, 233, 235, 245, 251

Offset: 1

Daniel Starodubtsev, Aug 14 2019

nonn

All terms are odd and not divisible by 3.

			11 is in the sequence because 11^2 - 12 = 109, which is prime.

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

Cf. A028870, A028873, A028876, A028879, A028882, A028885, A186815, A090696, A296507.

Cf. A056927.

Select[Range[5,301,2],PrimeQ[#^2-12]&] (* Harvey P. Dale, Dec 23 2019 *)

select(n->isprime(n^2-12), [1..1000]) \\ Andrew Howroyd, Aug 14 2019

If A056927(k) = 12, then k is a term. - A.H.M. Smeets, Aug 15 2019

cp's OEIS Frontend

A091271 Numbers k such that 4*k^2-11 is a prime.

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A091272 Primes of the form n^2 - 11.

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A091273 Indices of primes of the form k^2 - 11.

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A296507 Numbers m such that m^2 - 13 is a prime.

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A186815 Numbers n such that n^2-10 is a prime.

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Magma

Mathematica

A309726 Numbers k such that k^2 - 12 is prime.

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Mathematica

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