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A289363 Primes n such that n^2 + n - 1 is composite. 1
7, 17, 23, 29, 37, 43, 47, 61, 67, 71, 73, 79, 97, 107, 109, 113, 127, 137, 139, 151, 157, 167, 173, 179, 197, 211, 223, 227, 229, 239, 251, 257, 269, 271, 277, 283, 293, 307, 311, 313, 317, 337, 347, 353, 359, 367, 379, 383, 389, 397, 409, 421, 439, 443, 457, 467, 479, 487, 491, 503, 509, 521, 523 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Includes all primes == 2 (mod 5) or == 3 or 7 (mod 11) except 2 and 3.

If n is in this sequence, n^2 + n is not in A241884 although n^2 + n - 1 is composite.

LINKS

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

MAPLE

select(t -> isprime(t) and not isprime(t^2+t-1), [seq(i, i=1..1000, 2)]);

MATHEMATICA

Select[Prime[Range[100]], CompositeQ[#^2+#-1]&] (* Jean-Fran├žois Alcover, Jul 18 2017 *)

PROG

(PARI) lista(nn) = forprime(p=2, nn, if (!isprime(p^2+p-1), print1(p, ", "))); \\ Michel Marcus, Jul 05 2017

(MAGMA) [p: p in PrimesUpTo(600) | not IsPrime(p^2+p-1)]; // Vincenzo Librandi, Jul 05 2017

CROSSREFS

Cf. A241884.

Sequence in context: A191087 A032454 A107643 * A319040 A216838 A198441

Adjacent sequences:  A289360 A289361 A289362 * A289364 A289365 A289366

KEYWORD

nonn

AUTHOR

Robert Israel, Jul 04 2017

STATUS

approved

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Last modified July 12 13:34 EDT 2020. Contains 335663 sequences. (Running on oeis4.)