A267438 - OEIS

%I #14 Jan 27 2016 02:35:14

%S 11,23,67,151,487,2039,4211,524087,1046579,1073691427,1099510801043,

%T 2251799727348791,36028797132202711,4611686014335996451,

%U 36893488155919083943,147573952565445262007,604462909807989625559191,77371252455344850805618531,618970019642688992452665703,5070602400912917643802528801507

%N Abatzoglou-Silverberg-Sutherland-Wong primes: primes in A267437.

%C Abatzoglou, Silverberg, Sutherland, & Wong give a quasi-quadratic algorithm for determining membership in this sequence.

%H Charles R Greathouse IV, <a href="/A267438/b267438.txt">Table of n, a(n) for n = 1..42</a>

%H Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland, and Angela Wong, <a href="http://dx.doi.org/10.2140/obs.2013.1.1">Deterministic elliptic curve primality proving for a special sequence of numbers</a>, Tenth Algorithmic Number Theory Symposium (ANTS X, 2012), pp. 1-20.

%t Select[RecurrenceTable[{a[n] == 4 a[n - 1] - 7 a[n - 2] + 8 a[n - 3] - 4 a[n - 4], a[2] == 11, a[3] == 23, a[4] == 67, a[5] == 151}, a, {n, 2, 100}], PrimeQ] (* _Michael De Vlieger_, Jan 24 2016 *)

%o (PARI) A267437(n)=([0,1,0,0;0,0,1,0;0,0,0,1;-4,8,-7,4]^n*[11;11;23;67])[1,1]

%o list(lim)=my(v=List(),t,n); while((t=A267437(n++))<=lim, if(ispseudoprime(t), listput(v,t))); Vec(v)

%o (PARI) See Greathouse link in A267439.

%Y Cf. A267437, A267439.

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Jan 15 2016