A165682 Primes p such that 3*p*(p-1)+1 is also prime.
2, 3, 5, 7, 11, 29, 31, 43, 53, 59, 67, 89, 109, 137, 157, 173, 197, 239, 313, 347, 353, 389, 449, 521, 547, 557, 571, 577, 599, 613, 647, 677, 733, 743, 787, 857, 907, 941, 977, 1051, 1069, 1093, 1153, 1193, 1223, 1229, 1237, 1303, 1433, 1453, 1459, 1481, 1571
Offset: 1
Examples
For p=5 = a(3), 3*p^2-3*p+1=61 = A165683(3). For a(4)=p=7: 3*p^2-3*p+1=127 = A165684(4).
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Programs
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Magma
[p: p in PrimesUpTo(1600) | IsPrime(3*p*(p-1)+1)]; // Vincenzo Librandi, Apr 15 2013
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Mathematica
Select[Prime[Range[800]], PrimeQ[3 # (# - 1) + 1]&] (* Vincenzo Librandi, Apr 15 2013 *)
Formula
3*a(n)*(a(n)-1)+1 = A165683(n).
Extensions
2 and 3 inserted by R. J. Mathar, Sep 26 2009