A099806 - OEIS

A099806

If a,b are prime numbers satisfying the Diophantine equation a^3+b^3=c^2, then a is -1 mod 12 and b is 1 mod 12, or vice versa. Choose 'a' to be -1 mod 12. This is the sequence of 'a' values, sorted by the magnitude of c.

%I #5 Jun 17 2022 14:43:33

%S 11,8663,28703,56999,44111,86291,87959,16931,246011,54083,367823,

%T 552011,457511,571019,765983,1586531,1915163,2437751,16139,2305883,

%U 4074743,3963299,1296563,5440991,4683779,2238023,9682703,8681639,8142803

%N If a,b are prime numbers satisfying the Diophantine equation a^3+b^3=c^2, then a is -1 mod 12 and b is 1 mod 12, or vice versa. Choose 'a' to be -1 mod 12. This is the sequence of 'a' values, sorted by the magnitude of c.

%C All terms of this sequence are of the form 3*M^4-N^4+6*M^2*N^2 for some pair M,N of relatively prime positive integers of opposite parity.

%H James Buddenhagen, <a href="http://www.buddenbooks.com/jb/num_theory/sum_of_2_cubes_a_square.htm">Two Primes Cubed which Sum to a Square</a>.

%e 11 is in the sequence because 11 is -1 mod 12 and 11^3+37^3 = 228^2.

%Y Cf. A099807, A098970, A099808, A099809.

%K nonn

%O 0,1

%A _James R. Buddenhagen_, Oct 26 2004