A283359
Numbers of the form p^2 + q^2 = r^3 + s^3 with p, q, r, s primes.
Original entry on oeis.org
370, 7202, 36650, 1345682, 2127890, 2685962, 2715410, 3872090, 4331090, 4657490, 6379130, 7887458, 12235970, 14386538, 17938730, 19909370, 22588130, 22665530, 22694978, 30027170, 30080258, 31576970, 39707642, 40024010, 42567698, 42735530, 48438290, 54517538, 62572970, 72096050
Offset: 1
370=3^2+19^2=3^3+7^3, 7202=59^2+61^2=7^3+19^3.
A359447
a(n) is the least number that is the sum of two cubes of primes and is 2^n times an odd prime, or -1 if there is no such number.
Original entry on oeis.org
-1, -1, 152, 2224, 9056, 108736, -1, 4532992, 34674176, 268684288, 2280249344, 18693763072, 138890141696, 1111848828928, 8803419521024, 70375767212032, 564861779443712, 4507018424221696, 36030079546425344, 288238419152207872, 2305850719072157696, 18446757709572210688, 147573952867129622528
Offset: 1
a(3) = 152 because 3^3 + 5^3 = 152 = 2^3 * 19, 3 and 5 are primes and 19 is odd, and no smaller number works.
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f:= proc(n) local p,q,t;
t:= 2^n; p:= nextprime(t/2);
while p > 2 do
p:= prevprime(p);
q:= t - p;
if isprime(q) and isprime(p^2 - p*q + q^2) then return p^3 + q^3 fi
od;
-1
end proc:
map(f, [$1..20]);
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