A108656 - OEIS

%I #8 Dec 17 2013 11:40:23

%S 2,3,2,3,2,7,2,3,2,11,4,5,2,1,2,5,10,1,2,3,2,3,2,1,2,5,4,17,6,13,4,1,

%T 2,5,8,11,10,3,2,9,2,11,6,3,4,15,6,1,6,1,4,5,2,11,4,1,10,3,36,7,16,1,

%U 10,15,12,5,14,5,4,1,14,5,40,1,2,11,8,11,24,17,2,1,12,5,8,23,10,29,8,1,4,5

%N Least a(n)>0 such that a(n-2)*n^2+a(n-1)*n+a(n) is a prime.

%C Corresponding primes in A108657.

%H Harvey P. Dale, <a href="/A108656/b108656.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1)=2, a(2)=3 and a(3)=2 because 2*3^2+3*3+2=29 is aprime; a(4)=3, a(5)=2 and a(6)=7 because 3*6^2+2*6+7=127 is a prime.

%t a=2;b=3;s={a, b};Do[c=Prime[PrimePi[a*n^2+b*n]+1]-a*n^2-b*n;AppendTo[s, c];a=b;b=c, {n, 3, 200}];A108656=s

%t nxt[{n_,a_,b_}]:=Module[{c=a(n+1)^2+b(n+1)},{n+1,b,NextPrime[c]-c}]; Join[{2},Transpose[NestList[nxt,{2,2,3},100]][[3]]] (* _Harvey P. Dale_, Dec 17 2013 *)

%Y Cf. A108657.

%K nonn

%O 1,1

%A _Zak Seidov_, Jun 14 2005