A116214 Numbers n such that both n*(n+2)-(n+1) and n*(n+2)+(n+1) are primes.

2, 3, 4, 5, 8, 9, 10, 15, 19, 20, 30, 38, 44, 45, 53, 54, 55, 59, 64, 65, 85, 93, 100, 114, 125, 130, 140, 144, 148, 153, 154, 158, 159, 163, 180, 195, 218, 219, 230, 240, 258, 263, 264, 305, 330, 349, 350, 360, 373, 385, 395, 418, 419, 448, 449, 455, 473, 474

Offset

1,1

Comments

Sequence a(k)*(a(k)+2) = 8, 15, 24, 35, 80, 99, ... equals A069826.

Links

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

Example

20*22 = 440; both 440-21 = 419 and 440+21 = 461 are prime, hence 20 is a term.

Maple

select(n -> isprime(n^2+n-1) and isprime(n^2+3*n+1), [$1..1000]); # Robert Israel, Jun 11 2018

Mathematica

Select[Range@ 475, AllTrue[{# (# + 2) - (# + 1), # (# + 2) + (# + 1)}, PrimeQ] &] (* Michael De Vlieger, Jun 11 2018 *)

Prog

(Magma) [ n: n in [1..500] | IsPrime(n*(n+2)+(n+1)) and IsPrime(n*(n+2)-(n+1)) ]; /* Klaus Brockhaus, Apr 17 2007 */

Crossrefs

Cf. A005563 (n(n+2)), A069826 (numbers n such that sigma(n^2-n-1) = n*(n+1)).

Sequence in context: A087278 A054220 A337801 * A161389 A266118 A287802

Adjacent sequences: A116211 A116212 A116213 * A116215 A116216 A116217

Keyword

nonn

Author

J. M. Bergot, Apr 16 2007

Extensions

Edited and extended by Klaus Brockhaus, Apr 17 2007

Status

approved