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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
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 *) -
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
Formula
a(n) ~ n. - Charles R Greathouse IV, Aug 30 2017
Comments