

A116214


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


2



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
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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 44021 = 419 and 440+21 = 461 are prime, hence 20 is a term.


MAPLE

select(n > isprime(n^2+n1) 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^2n1) = n*(n+1)).
Sequence in context: A087278 A054219 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



