A290767 - OEIS

A290767

Primes p such that p^2 +/- p +/- 1 are all nonprimes.

23, 37, 43, 73, 107, 109, 113, 137, 157, 179, 211, 223, 227, 229, 239, 251, 257, 271, 277, 283, 311, 313, 317, 347, 353, 367, 389, 439, 443, 467, 503, 509, 521, 523, 547, 557, 563, 577, 587, 593, 601, 631, 653, 661, 719, 733, 757, 797, 811, 821, 823, 829, 853, 859, 877, 883

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OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

Intersection of the complements of A053184, A053182, A065508, and A091567 within the primes A000040.

MAPLE

select(p -> isprime(p) and not ormap(isprime, [p^2+p+1, p^2+p-1, p^2-p+1, p^2-p-1]), [2, seq(i, i=3..1000, 2)]); # Robert Israel, Aug 10 2017

MATHEMATICA

Select[Prime[Range[1000]], ! (PrimeQ[#^2 + # + 1] || PrimeQ[#^2 + # - 1] ||PrimeQ[#^2 - # + 1] || PrimeQ[#^2 - # - 1]) &]

Select[Prime[Range[200]], NoneTrue[{#^2+#+1, #^2+#-1, #^2-#+1, #^2-#-1}, PrimeQ]&] (* Harvey P. Dale, Oct 13 2024 *)

PROG

(PARI) is(n) = my(v=[n^2+n+1, n^2+n-1, n^2-n+1, n^2-n-1]); for(k=1, #v, if(ispseudoprime(v[k]), return(0))); 1

forprime(p=1, 900, if(is(p), print1(p, ", "))) \\ Felix Fröhlich, Aug 10 2017

CROSSREFS

Cf. A000040, A053184, A053182, A065508, A091567, A236056.

Sequence in context: A163384 A291689 A059798 * A173829 A110673 A134797

Adjacent sequences: A290764 A290765 A290766 * A290768 A290769 A290770

KEYWORD

nonn

AUTHOR

Ralf Steiner, Aug 10 2017

STATUS

approved