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A291689 Numbers n such that n^2 +- n +- 1 are all composite. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 29 16:13 EDT 2020. Contains 337432 sequences. (Running on oeis4.)