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Numbers k such that 1 + 2k + 3k^2 is prime.
8

%I #15 Jan 09 2019 01:53:47

%S 2,12,14,18,24,26,32,38,44,56,62,68,90,92,98,114,120,126,128,144,150,

%T 158,164,168,170,176,180,186,192,200,210,212,216,230,246,254,260,266,

%U 276,278,282,290,300,318,332,344,354,362,366,378,396,398,408,420,432

%N Numbers k such that 1 + 2k + 3k^2 is prime.

%C Excluding a(1), these are also the bases in which 321 represents a prime number.

%H Harvey P. Dale, <a href="/A086285/b086285.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Range[500],PrimeQ[1+2#+3#^2]&] (* _Harvey P. Dale_, Jun 23 2012 *)

%o (PARI) is(n)=isprime(1+2*n+3*n^2) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A056109 (3n^2+2n+1).

%K easy,nonn

%O 1,1

%A _Zak Seidov_, Aug 28 2003