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 A165683 Primes of form 3*p*(p-1)+1 with p also a prime. 3

%I #13 Sep 08 2022 08:45:48

%S 7,19,61,127,331,2437,2791,5419,8269,10267,13267,23497,35317,55897,

%T 73477,89269,115837,170647,292969,360187,372769,452797,603457,812761,

%U 895987,929077,976411,997057,1074607,1125469,1253887,1372957,1609669,1653919

%N Primes of form 3*p*(p-1)+1 with p also a prime.

%H Vincenzo Librandi, <a href="/A165683/b165683.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = x^3-(x-1)^3 where x = A165682(n).

%e a(3)= 61=3*5*(5-1)+1 generated by p=3. a(4)=127=3*7*(7-1)+1 generated by p=7. a(5)=331=3*11*(11-1)+1.

%t Select[Table[3 p (p - 1) + 1, {p, Prime[Range[100]]}], PrimeQ] (* _Vincenzo Librandi_, Sep 13 2013 *)

%o (Magma) [a: p in PrimesUpTo(1000) | IsPrime(a) where a is 3*p*(p-1)+1]; // _Vincenzo Librandi_, Sep 13 2013 *

%Y Cf. A165681, A165682.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Sep 24 2009

%E 7 and 19 inserted by _R. J. Mathar_, Sep 26 2009

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Last modified August 7 13:33 EDT 2024. Contains 375013 sequences. (Running on oeis4.)