A137459 Prime numbers n such that n^2 +- (n-1) are primes.

2, 3, 13, 163, 193, 349, 541, 769, 1093, 1231, 1423, 1549, 1621, 1693, 1801, 2011, 3049, 3511, 4003, 4111, 4159, 5839, 6091, 6421, 6703, 6883, 7573, 7753, 8929, 9043, 9601, 9769, 9781, 12781, 13633, 14821, 15091, 15439, 16141, 16759, 17863, 18493

Offset

1,1

Links

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

Example

2^2 +- 1 -> (3,4) Primes,
3^2 +- 2 -> (7,11) Primes,
13^2 +- 12 -> (157,181) Prime

Mathematica

Select[Prime[Range[800]], PrimeQ[ #^2-(#-1)]&&PrimeQ[ #^2+(#-1)]&]
Select[Prime[Range[2500]], AllTrue[#^2+{(#-1), (1-#)}, PrimeQ]&] (* Harvey P. Dale, Jul 15 2023 *)

Crossrefs

Sequence in context: A062447 A153888 A068083 * A267422 A072162 A113785

Adjacent sequences: A137456 A137457 A137458 * A137460 A137461 A137462

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2008

Extensions

More terms from Stefan Steinerberger, Apr 26 2008

Status

approved