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, 13032949, 12140509, 7480657, 10079917, 4518469, 17370817

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. 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.

Links

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

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

Example

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

Crossrefs

Cf. A099806, A098970, A099808, A099809.

Sequence in context: A025762 A297313 A297505 * A193123 A295846 A386540

Adjacent sequences: A099804 A099805 A099806 * A099808 A099809 A099810

Keyword

nonn

Author

James R. Buddenhagen, Oct 26 2004

Extensions

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

Status

approved