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.

11, 8663, 28703, 56999, 44111, 86291, 87959, 16931, 246011, 54083, 367823, 552011, 457511, 571019, 765983, 1586531, 1915163, 2437751, 16139, 2305883, 4074743, 3963299, 1296563, 5440991, 4683779, 2238023, 9682703, 8681639, 8142803, 10185443, 13810031, 16204883, 18800363, 12132671, 20568083

Offset

0,1

Comments

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.

Links

Zhining Yang, Table of n, a(n) for n = 0..79

James Buddenhagen, Two Primes Cubed which Sum to a Square.

Example

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

Crossrefs

Cf. A099807, A098970, A099808, A099809.

Sequence in context: A320984 A080050 A067254 * A227063 A286197 A287078

Adjacent sequences: A099803 A099804 A099805 * A099807 A099808 A099809

Keyword

nonn

Author

James R. Buddenhagen, Oct 26 2004

Extensions

a(29)-a(34) from Zhining Yang, Mar 26 2026

Status

approved