A161863 -id:A161863 - cp's OEIS frontend

A161864 Numbers n such that n^2 + n + 5 and n^2 + n - 5 are both prime.

3, 6, 11, 18, 21, 23, 27, 32, 42, 48, 51, 83, 86, 93, 116, 153, 158, 182, 188, 216, 282, 291, 317, 333, 396, 482, 681, 737, 786, 798, 818, 821, 872, 923, 956, 966, 977, 986, 1007, 1026, 1077, 1082, 1106, 1161, 1287, 1292, 1302, 1337, 1341, 1451, 1467, 1563

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jun 20 2009

			a(1)=3 as 12+-5 are primes. a(2)=6 as 42+-5 are primes.

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

Cf. A088485, A161863.

select(n -> isprime(n^2+n+5) and isprime(n^2+n-5), [$1..2000]); # Robert Israel, Nov 26 2017

q=5;lst5={};Do[p=n^2+n;If[PrimeQ[p-q]&&PrimeQ[p+q],AppendTo[lst5,n]], {n,0,7!}];lst5

Definition rephrased by R. J. Mathar, Jun 23 2009

A161866 Numbers k such that k^2+k+7 and k^2+k-7 are both prime.

Original entry on oeis.org

3, 5, 9, 12, 24, 29, 32, 39, 44, 50, 57, 59, 65, 102, 135, 137, 144, 170, 180, 207, 260, 267, 297, 302, 305, 344, 347, 360, 365, 369, 389, 404, 429, 464, 474, 495, 540, 555, 570, 612, 620, 659, 662, 689, 767, 774, 792, 824, 837, 872, 885, 900, 950, 954, 989

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jun 20 2009

			a(1)=3 as 12+-7 are primes. a(2)=5 as 30+-7 are primes.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A088485, A161863, A161864, A153417.

[k:k in [1..1000]| IsPrime(k^2+k+7) and IsPrime(k^2+k-7)]; // Marius A. Burtea, Feb 17 2020

q=7;lst7={};Do[p=n^2+n;If[PrimeQ[p-q]&&PrimeQ[p+q],AppendTo[lst7,n]], {n,0,7!}];lst7
Select[Range[1000],AllTrue[#^2+#+{7,-7},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 26 2021 *)

Definition rephrased by R. J. Mathar, Jun 23 2009

cp's OEIS Frontend

A161864 Numbers n such that n^2 + n + 5 and n^2 + n - 5 are both prime.

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