A173875 - OEIS

%I #12 Sep 08 2022 08:45:50

%S 5,11,59,1439,2459,2819,3119,4079,4799,5399,5879,6899,7559,12539,

%T 13799,14159,16139,19379,25919,27239,28019,28499,29759,39119,40739,

%U 41519,42179,44159,44939,46919,53759,57119,60539,63599,64019,65579,66359

%N Primes p of the form a^2-b^2 and p*a-b is also prime (with b=prime and a=b+1).

%H Vincenzo Librandi, <a href="/A173875/b173875.txt">Table of n, a(n) for n = 1..300</a>

%F A005385 INTERSECT A048161. [_R. J. Mathar_, Mar 29 2010]

%e p=11 is in this sequence because 6^2-5^2=11 and 11*6-5=61.

%e 4799 is in this sequence because 2400^2-2399^2=4799 and 4799*2400-2399=11515201.

%t Select[Prime[Range[10000]], PrimeQ[(# - 1)/2] &&PrimeQ[ (#^2 + 1)/2] &] (* _Vincenzo Librandi_, Aug 21 2014 *)

%o (Magma) [p: p in PrimesUpTo(10^5) | IsPrime((p-1) div 2) and IsPrime((p^2+1) div 2)]; // _Vincenzo Librandi_ Aug 21 2014

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Mar 06 2010

%E Missing terms inserted and sequence extended by _R. J. Mathar_, Mar 29 2010