A349987 Numbers that can be represented in more than one way as p^2+p*q+q^2 with p and q primes, p<=q.

147, 903, 1911, 3667, 3913, 4627, 5187, 8103, 10137, 11613, 12999, 13117, 13467, 14313, 16023, 16887, 18723, 19047, 19747, 20397, 22197, 23107, 24307, 25833, 28227, 30457, 30847, 31827, 32403, 37947, 38703, 39819, 45163, 46543, 50407, 57603, 58813, 61383, 63147, 68367, 68403, 70707, 71337, 74973

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 09 2022

Keywords

• nonn

Examples

			a(3) = 1911 is a term because 1911 = 5^2+5*41+41^2 = 19^2+19*31+31^2 where 5, 41, 19 and 31 are primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2500

Crossrefs

Subsequence of A024614.

Cf. A349986.

Programs

Maple

N:= 10^6: # for terms <= N
P:= select(isprime, [2,seq(i,i=3..floor(sqrt(N)),2)]):
nP:= nops(P):
S:= {}: T:= {}:
for i from 1 to nP do
  for j from 1 to i do
    x:= P[i]^2 + P[i]*P[j]+P[j]^2;
    if x > N then break fi;
    if member(x,S) then T:= T union {x} fi;
    S:= S union {x};
od od:
sort(convert(T,list));

Mathematica

Do[If[Total@Boole[And@@@PrimeQ[{p,q}/.Solve[p^2+p*q+q^2==k&&p>1&&p<=q,{p,q},Integers]]]>1,Print@k],{k,10^6}] (* Giorgos Kalogeropoulos, Jan 09 2022 *)