A259142 Least prime p of the form n*q^2+(n+1)*r^2 with q and r prime.

17, 83, 43, 61, 149, 199, 263, 113, 331, 139, 383, 373, 173, 191, 199, 569, 587, 547, 251, 269, 277, 757, 1223, 1321, 859, 347, 787, 373, 3779, 1789, 1063, 953, 433, 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

Offset: 1

Author

Zak Seidov, Jun 19 2015

Keywords

• nonn
• look

Comments

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}.

a(2) = A084866(1). - Michel Marcus, Jun 20 2015

For p in A093191, a((p-4)/13) = p. - Robert Israel, Apr 30 2018

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Zak Seidov, First 100 values of {p,q,r}.

Crossrefs

Cf. A000040, A093191.

Programs

Maple

P:= [seq(ithprime(i),i=1..20)]: np:= 20:
for n from 1 to 100 do
  found:= false;
  while not found do
    R:= sort([seq(seq(n*q^2+(n+1)*p^2,p=P),q=P)]);
    w:= n*4+(n+1)*P[-1]^2+1;
    r:= ListTools:-SelectFirst(isprime,R);
    if r <> NULL and r <= w then
      A[n]:= r;
      found:= true;
    else
      P:= [op(P), seq(ithprime(i),i=np+1..np+20)];
      np:= np+20;
    fi
  od;
od:
seq(A[i],i=1..100); # Robert Israel, Apr 30 2018