Cilleruelo, Luca, and Pizarro show that a(1) = 27 and that this sequence is of density 0. They give an explicit upper bound for any such Carmichael number, though it is too large to be of computational use.
Terms after the first are conjectural. a(2) could be proved by an argument like that on p. 17 on 33 with the addition of the prime 257 (29 and 31 are not in this sequence by 7.1).
This sequence is infinite, since each member is associated to finitely many Carmichael numbers and there are infinitely many Carmichael numbers.
|