A226191 Odd numbers n such that n*2^k + 1 is a Carmichael number for some k.

27, 35, 69, 77, 255

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..5.

Javer Cilleruelo, Florian Luca, and Amalia Pizarro, Carmichael numbers in the sequence {k*2^n+1}_{n >= 1} (2013)

Example

27 is a member because 27*2^6 + 1 = 1729 is a Carmichael number.

Crossrefs

Cf. A002997.

Sequence in context: A164376 A025583 A134101 * A098883 A326893 A160119

Adjacent sequences: A226188 A226189 A226190 * A226192 A226193 A226194

Keyword

nonn

Author

Charles R Greathouse IV, May 30 2013

Status

approved