A366703 List of quadruples (a,b,c,d) with a^4 + b^4 = c^4 + d^4, a < c < d < b, a,b,c,d prime, listed in order of the largest term b.

7, 239, 157, 227, 40351, 62047, 46747, 59693

Offset

1,1

Comments

See A255352 for quadruples which do not necessarily consist of prime numbers. There are infinitely many such quadruples, because if (a, b, c, d) is in the sequence, so is (m*a, m*b, m*c, m*d). It is unknown whether there are infinitely many quadruples which consist only of prime numbers. The two given quadruples are the only ones with a^4 + b^4 = c^4 + d^4 <= 10^24.

Links

Table of n, a(n) for n=1..8.

Mia Müßig, Julia code for finding general taxicab numbers.

Example

The quadruples (a,b,c,d), listed in order of increasing b = max{a,b,c,d}, are
  (7, 239, 157, 227),
  (40351, 62047, 46747, 59693), ...

Crossrefs

Cf. A018786, A255351, A255352.

Sequence in context: A287042 A160491 A120661 * A185389 A159967 A349046

Adjacent sequences: A366700 A366701 A366702 * A366704 A366705 A366706

Keyword

nonn,hard,more

Author

Mia Muessig, Oct 17 2023

Status

approved