A173875 Primes p of the form a^2-b^2 and p*a-b is also prime (with b=prime and a=b+1).

5, 11, 59, 1439, 2459, 2819, 3119, 4079, 4799, 5399, 5879, 6899, 7559, 12539, 13799, 14159, 16139, 19379, 25919, 27239, 28019, 28499, 29759, 39119, 40739, 41519, 42179, 44159, 44939, 46919, 53759, 57119, 60539, 63599, 64019, 65579, 66359

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Formula

A005385 INTERSECT A048161. [R. J. Mathar, Mar 29 2010]

Example

p=11 is in this sequence because 6^2-5^2=11 and 11*6-5=61.
4799 is in this sequence because 2400^2-2399^2=4799 and 4799*2400-2399=11515201.

Mathematica

Select[Prime[Range[10000]], PrimeQ[(# - 1)/2] &&PrimeQ[ (#^2 + 1)/2] &] (* Vincenzo Librandi, Aug 21 2014 *)

Prog

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

Crossrefs

Sequence in context: A057824 A057822 A168243 * A095150 A215759 A041697

Adjacent sequences: A173872 A173873 A173874 * A173876 A173877 A173878

Keyword

nonn

Author

Vincenzo Librandi, Mar 06 2010

Extensions

Missing terms inserted and sequence extended by R. J. Mathar, Mar 29 2010

Status

approved