A349986 Numbers that can be represented as p^2 + p*q + q^2 where p and q are primes.

12, 19, 27, 39, 49, 67, 75, 79, 109, 147, 163, 199, 201, 217, 247, 259, 309, 327, 349, 363, 399, 403, 427, 433, 457, 481, 507, 543, 579, 597, 607, 669, 679, 691, 739, 777, 867, 903, 937, 973, 997, 1011, 1027, 1063, 1083, 1093, 1141, 1209, 1227, 1281, 1327, 1387, 1423, 1447, 1489, 1533, 1579, 1587

Offset

1,1

Comments

The only square in this sequence is 49.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Mathematics StackExchange, Largest square written as p^2+pq+q^2 where p, q are primes?

Example

a(3) = 27 is a term because 27 = 3^2+3*3+3^2.
a(4) = 39 is a term because 39 = 2^2+2*5+5^2.

Maple

N:= 10^4: # for terms <= N
P:= select(isprime, [2, seq(i, i=3..floor(sqrt(N)), 2)]):
nP:= nops(P):
S:= {}:
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;
    S:= S union {x};
od od:
sort(convert(S, list));

Crossrefs

Contains A079705, A244146, A349987.

Subsequence of A024614.

Sequence in context: A030609 A053752 A291939 * A043102 A039279 A045067

Adjacent sequences: A349983 A349984 A349985 * A349987 A349988 A349989

Keyword

nonn

Author

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

Status

approved