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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Subsequence of A024614.

Cf. A349986.

Sequence in context: A063701 A261939 A251107 * A183741 A020328 A075925

Adjacent sequences: A349984 A349985 A349986 * A349988 A349989 A349990

Keyword

nonn

Author

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

Status

approved