A137474 - OEIS

%I #18 Sep 08 2022 08:45:32

%S 3,7,13,73,97,157,523,1483,1993,2521,3967,5641,6607,7717,8761,9397,

%T 11821,11971,12241,12613,13597,14083,15511,16231,16411,17203,17293,

%U 19801,23143,23167,23857,28123,29173,29881,30391,31477,31723,32323

%N Prime numbers p such that p^3 - (p-1)^2 and p^3 + (p-1)^2 are also primes.

%H Daniel Starodubtsev, <a href="/A137474/b137474.txt">Table of n, a(n) for n = 1..10000</a>

%e p=7: 7^3 - (7-1)^2 = 307 is prime and 7^3 + (7-1)^2 = 379 is prime, hence 7 is in the sequence.

%t Select[Prime[Range[900]],PrimeQ[ #^3-(#-1)^2]&&PrimeQ[ #^3+(#-1)^2]&]

%o (Magma) [ n: n in PrimesUpTo(40000) | IsPrime(n^3-(n-1)^2) and IsPrime(n^3 +(n-1)^2) ]; // _Vincenzo Librandi_, Nov 24 2010

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 21 2008

%E More terms from _Vincenzo Librandi_, Mar 26 2010