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%I #9 Jan 03 2014 01:50:07
%S 27,35,69,77,255
%N Odd numbers n such that n*2^k + 1 is a Carmichael number for some k.
%C 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.
%C 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).
%C This sequence is infinite, since each member is associated to finitely many Carmichael numbers and there are infinitely many Carmichael numbers.
%H Javer Cilleruelo, Florian Luca, and Amalia Pizarro, <a href="http://arxiv.org/abs/1305.3580">Carmichael numbers in the sequence {k*2^n+1}_{n >= 1}</a> (2013)
%e 27 is a member because 27*2^6 + 1 = 1729 is a Carmichael number.
%Y Cf. A002997.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_, May 30 2013
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