A069224 Numbers n such that n^2 + n + A007918(n+2) is prime.

1, 2, 3, 5, 6, 7, 8, 9, 12, 13, 14, 15, 20, 30, 32, 35, 36, 37, 38, 39, 44, 47, 49, 56, 60, 63, 65, 66, 75, 80, 84, 90, 93, 96, 98, 102, 104, 110, 113, 117, 119, 125, 129, 130, 133, 139, 140, 145, 146, 149, 150, 153, 155, 159, 162, 167, 170, 179, 180, 183, 184, 192

Offset: 1

Author

Michael V. Scovetta (mike(AT)scovetta.com), Apr 12 2002

Keywords

• nonn

Comments

Let K be the number of entries in the sequence less than or equal to M. Then the ratio K/M is nearly monotone decreasing. I do not know if the sequence converges, but if it does, it will be to a number less than 0.30.

Examples

			35 is a term because 35^2 + 35 + 37 = 1297, which is prime.
		

Links

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

Crossrefs

Cf. A007918.

Programs

Magma

[n: n in [1..200] | IsPrime(n^2 + n + NextPrime(n+1))]; // Vincenzo Librandi, Aug 11 2018

Maple

filter:= select(n -> isprime(n^2+n+nextprime(n+1)), [$1..200]); # Robert Israel, Aug 10 2018

Mathematica

Select[Range[200], PrimeQ[(NextPrime[# + 1] + #^2 + #)] &] (* Vincenzo Librandi, Aug 11 2018 *)

PARI

isok(n) = isprime(n^2 + n + nextprime(n+2)); \\ Michel Marcus, Aug 11 2018

Extensions

1 inserted, and definition corrected by Robert Israel, Aug 10 2018