A259142 - OEIS

%I #12 May 01 2018 02:44:52

%S 17,83,43,61,149,199,263,113,331,139,383,373,173,191,199,569,587,547,

%T 251,269,277,757,1223,1321,859,347,787,373,3779,1789,1063,953,433,

%U 1181,1019,1069,1283,503,2311,5209,1193,1453,563,1301,2389,607,1367,1657,641,659,1483,1777,1811,1861,719,1913,1657,1997,4391,3229,797,1823

%N Least prime p of the form n*q^2+(n+1)*r^2 with q and r prime.

%C Values of {p,q,r}: {17,3,2},{83,2,5},{43,3,2},{61,2,3},{149,5,2},{199,2,5},{263,3,5},{113,2,3}.

%C a(2) = A084866(1). - _Michel Marcus_, Jun 20 2015

%C For p in A093191, a((p-4)/13) = p. - _Robert Israel_, Apr 30 2018

%H Robert Israel, <a href="/A259142/b259142.txt">Table of n, a(n) for n = 1..10000</a>

%H Zak Seidov, <a href="/A259142/a259142.txt">First 100 values of {p,q,r}.</a>

%e 17=1*3^2+2*2^2, 83=2*2^2+3*5^2, 43=3*3^2+4*2^2.

%p P:= [seq(ithprime(i),i=1..20)]: np:= 20:

%p for n from 1 to 100 do

%p   found:= false;

%p   while not found do

%p     R:= sort([seq(seq(n*q^2+(n+1)*p^2,p=P),q=P)]);

%p     w:= n*4+(n+1)*P[-1]^2+1;

%p     r:= ListTools:-SelectFirst(isprime,R);

%p     if r <> NULL and r <= w then

%p       A[n]:= r;

%p       found:= true;

%p     else

%p       P:= [op(P), seq(ithprime(i),i=np+1..np+20)];

%p       np:= np+20;

%p     fi

%p   od;

%p od:

%p seq(A[i],i=1..100); # _Robert Israel_, Apr 30 2018

%Y Cf. A000040, A093191.

%K nonn,look

%O 1,1

%A _Zak Seidov_, Jun 19 2015