A099807 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 'b' to be 1 mod 12. This is the sequence of 'b' values, sorted by the magnitude of c.

37, 2137, 8929, 1801, 48817, 6637, 57241, 133597, 151477, 334717, 3889, 127717, 786697, 735781, 1154017, 38557, 1662229, 2446777, 3882661, 3811669, 2747449, 3716701, 5634637, 3600097, 9836221, 10591849, 7139569, 9473161, 11395309

Offset: 0

Author

James R. Buddenhagen, Oct 26 2004

Keywords

• nonn

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. For each n, a=A099806[n], b=A099807[n] are prime numbers and a^3 + b^3 = c^2, for some integer c. c is divisible by 12 and A098970 gives the values of c/12.

Examples

			37 is in the sequence because 37 is a prime congruent to 1 mod 12 and 11^3+37^3=228^2.
		

Links

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

Crossrefs

Cf. A099806, A098970, A099808, A099809.