A291689 Numbers n such that n^2 +- n +- 1 are all composite.

23, 37, 43, 52, 73, 74, 82, 88, 92, 98, 107, 108, 109, 113, 122, 123, 124, 128, 129, 133, 136, 137, 152, 157, 166, 178, 179, 183, 198, 201, 202, 205, 208, 211, 212, 213, 214, 217, 222, 223, 224, 227, 228, 229, 235, 238, 239, 243, 250, 251, 252, 253, 254, 255, 256, 257, 261, 262, 270, 271, 274

Offset

1,1

Comments

Numbers n such that A291654(n)=1.

Complement of union of A002328, A002384, A045546 and A055494.

Links

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

Formula

a(n) ~ n. - Charles R Greathouse IV, Aug 30 2017

Example

a(1)=23 is in the sequence because 23^2 - 23 - 1 = 505, 23^2 - 23 + 1 = 507, 23^2 + 23 - 1 = 551, 23^2 + 23 + 1 = 553 are all composite.

Maple

select(t -> not ormap(isprime, {t^2+t+1, t^2+t-1, t^2-t+1, t^2-t-1}), [$1..1000]);

Mathematica

Select[Range@ 300, Function[t, AllTrue[t^2 + Map[Total[{t, 1} #] &, Tuples[{1, -1}, 2]], ! PrimeQ@ # &]]] (* Michael De Vlieger, Aug 29 2017 *)

Prog

(PARI) is(n)=my(n2=n^2); !isprime(n2+n+1) && !isprime(n2+n-1) && !isprime(n2-n+1) && !isprime(n2-n-1) \\ Charles R Greathouse IV, Aug 30 2017

Crossrefs

Cf. A002328, A002384, A045546, A055494, A291654.

Sequence in context: A329179 A154114 A163384 * A059798 A290767 A173829

Adjacent sequences: A291686 A291687 A291688 * A291690 A291691 A291692

Keyword

nonn

Author

Robert Israel, Aug 29 2017

Status

approved