A154939 Primes p such that (p-1)*(p+1)-+p are primes.

3, 5, 11, 31, 101, 131, 149, 181, 241, 331, 419, 449, 709, 1051, 1061, 1171, 1409, 1549, 1579, 1699, 1759, 1831, 2069, 3229, 3449, 3761, 3911, 4159, 4951, 5821, 6029, 6481, 6661, 6679, 6899, 7079, 7151, 7229, 7369, 8101, 8219, 8629, 8861, 9091, 9161, 9521

Offset

1,1

Comments

That is, primes p such that p^2+p-1 and p^2-p-1 are both primes: intersection of A053184 and A091567. - Michel Marcus, Jul 10 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

2*4=8-+3 -> primes, 4*6=24-+5 -> primes,...

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[(p-1)*(p+1)-p]&&PrimeQ[(p-1)*(p+1)+p], AppendTo[lst, p]], {n, 7!}]; lst
Select[Prime[Range[1500]], And@@PrimeQ/@{#^2 - # - 1, #^2 + # - 1} &] (* Vincenzo Librandi, Jul 10 2016 *)
Select[Prime[Range[1500]], AllTrue[(#-1)(#+1)+{#, -#}, PrimeQ]&] (* Harvey P. Dale, Sep 21 2023 *)

Prog

(Magma) [p: p in PrimesUpTo(10000) | IsPrime(p^2+p-1) and IsPrime(p^2-p-1)]; // Vincenzo Librandi, Jul 10 2016

Crossrefs

Cf. A053184, A038872, A141158, A091567, A098058, A038936, A089270, A140559.

Sequence in context: A236568 A095184 A048235 * A121926 A063499 A285381

Adjacent sequences: A154936 A154937 A154938 * A154940 A154941 A154942

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 17 2009

Status

approved