|
%I #13 Dec 05 2020 04:39:12
%S 457871,685031,1029071,1101431,9407831,11769911,18437999
%N Locations of primes in the Fourier expansion of the j-function: numbers k such that A000521(k) is prime.
%C All terms up to 2*10^7 are listed. It is unknown if the sequence is infinite.
%C Jeremy Rouse reports having certified the primality of the first entry using ECPP. The remaining primes pass a BPSW test.
%C The corresponding prime numbers A000521(a(n)) have 3689, 4513, 5532, 5723, 16734, 18718, 23429 digits.
%H D. Feldman, <a href="https://mathoverflow.net/questions/377061">Does the Fourier expansion of the j-function have any prime coefficients?</a>, MathOverflow, 2020.
%H F. Johansson, <a href="https://arxiv.org/abs/2011.14671">Computing isolated coefficients of the j-function</a>, arXiv:2011.14671 [math.NT], 2020.
%H F. Johansson, <a href="https://github.com/fredrik-johansson/jfunction">Data files and source code for computations</a>.
%e c_457871 is the first prime in the sequence c_n = A000521(n).
%Y Cf. A000521.
%K nonn,more
%O 1,1
%A _Fredrik Johansson_, Dec 04 2020
| 