A350655 a(n) is the least positive number that can be written as p^2 + p*q + q^2 in exactly n ways where p and q are primes and p <= q.

1, 12, 147, 57603, 160797, 4611243, 36822513, 878112417, 2069618187, 9891199227, 9098192883, 27885254943, 73104587283, 132014176203, 3457814397303, 1449081095007, 5644476547437, 9051074413563, 31516441411377, 8343886414773, 5272121828883

Offset

0,2

Comments

a(9) > 5*10^9. - Jon E. Schoenfield, Jan 13 2022

Links

Table of n, a(n) for n=0..20.

Example

a(3) = 57603 as 57603 has the three representations 57603 = 2^2 + 2*239 + 239^2 = 31^2 + 31*223 + 223^2 = 101^2 + 101*173 + 173^2 and no smaller number has this property.

Maple

N:= 10^9:
Q:= Vector(N, datatype=integer[4]):
P:= select(isprime, [2, seq(i, i=3..floor(sqrt(N)), 2)]):
T:= Array(0..7): T[0]:= 1:
nP:= nops(P):
for i from 1 to nP do
  for j from 1 to i do
    v:= P[i]^2 + P[i]*P[j] + P[j]^2;
    if v > N then break fi;
    Q[v]:= Q[v]+1;
    if T[Q[v]] = 0 or v < T[Q[v]] then T[Q[v]]:= v fi
od od:
convert(T, list);

Crossrefs

Cf. A349987.

Sequence in context: A039493 A196454 A329013 * A167138 A001406 A057572

Adjacent sequences: A350652 A350653 A350654 * A350656 A350657 A350658

Keyword

nonn,more

Author

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

Extensions

a(8) from Jon E. Schoenfield, Jan 13 2022

a(9)-a(20) from Martin Ehrenstein, Jan 24 2022

Status

approved