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A165682 Primes p such that 3*p*(p-1)+1 is also prime. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

3*a(n)*(a(n)-1)+1 = A165683(n).

EXAMPLE

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).

MATHEMATICA

Select[Prime[Range[800]], PrimeQ[3 # (# - 1) + 1]&] (* Vincenzo Librandi, Apr 15 2013 *)

PROG

(MAGMA) [p: p in PrimesUpTo(1600) | IsPrime(3*p*(p-1)+1)]; // Vincenzo Librandi, Apr 15 2013

CROSSREFS

Cf. A165681, A165683.

Sequence in context: A036342 A114421 A167119 * A296924 A175711 A099160

Adjacent sequences:  A165679 A165680 A165681 * A165683 A165684 A165685

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Sep 24 2009

EXTENSIONS

2 and 3 inserted by R. J. Mathar, Sep 26 2009

STATUS

approved

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Last modified February 26 17:19 EST 2020. Contains 332293 sequences. (Running on oeis4.)