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Primes of the form 1+2*n+3*n^2.
3

%I #27 Sep 08 2022 08:45:28

%S 17,457,617,1009,1777,2081,3137,4409,5897,9521,11657,14009,24481,

%T 25577,29009,39217,43441,47881,49409,62497,67801,75209,81017,85009,

%U 87041,93281,97561,104161,110977,120401,132721,135257,140401,159161,182041

%N Primes of the form 1+2*n+3*n^2.

%C 3*a(n)-2 is a square (of the form (3*k+1)^2). - _Vincenzo Librandi_, Mar 15 2013

%C Also primes which are the sum of 2 consecutive pentagonal numbers (A000326). - _Vicente Izquierdo Gomez_, Aug 13 2017

%H Vincenzo Librandi, <a href="/A122430/b122430.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Table[1 + 2 n + 3 n^2, {n, 500}], PrimeQ] (* _Vincenzo Librandi_, Mar 15 2013 *)

%o (Magma) [a: n in [1..300] | IsPrime(a) where a is 1+2*n+3*n^2]; // _Vincenzo Librandi_, Mar 15 2013

%o (PARI) is(n)=isprime(n) && issquare(3*n-2,&n) && n%3==1 \\ _Charles R Greathouse IV_, Sep 23 2013

%Y Cf. A086285 (numbers n such that 1+2n+3n^2 is prime).

%Y Subsequence of A056109.

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 20 2006