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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..28.

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 A297719

Adjacent sequences:  A099804 A099805 A099806 * A099808 A099809 A099810

KEYWORD

nonn

AUTHOR

James R. Buddenhagen, Oct 26 2004

STATUS

approved

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Last modified September 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)