Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Oct 18 2023 10:04:24
%S 7,239,157,227,40351,62047,46747,59693
%N 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.
%C 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.
%H Mia Müßig, <a href="https://github.com/PhoenixSmaug/taxicab-numbers">Julia code for finding general taxicab numbers</a>.
%e The quadruples (a,b,c,d), listed in order of increasing b = max{a,b,c,d}, are
%e (7, 239, 157, 227),
%e (40351, 62047, 46747, 59693), ...
%Y Cf. A018786, A255351, A255352.
%K nonn,hard,more
%O 1,1
%A _Mia Muessig_, Oct 17 2023