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

%I #12 Aug 30 2017 01:54:12

%S 23,37,43,52,73,74,82,88,92,98,107,108,109,113,122,123,124,128,129,

%T 133,136,137,152,157,166,178,179,183,198,201,202,205,208,211,212,213,

%U 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

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

%C Numbers n such that A291654(n)=1.

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

%H Robert Israel, <a href="/A291689/b291689.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ n. - _Charles R Greathouse IV_, Aug 30 2017

%e 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.

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

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

%o (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

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

%K nonn

%O 1,1

%A _Robert Israel_, Aug 29 2017

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Last modified March 28 08:12 EDT 2024. Contains 371236 sequences. (Running on oeis4.)