A086258 a(n) is the smallest k such that 2^k+1 has n primitive prime factors.

0, 14, 26, 46, 83, 118, 309, 194, 414, 538, 786, 958

Offset

1,2

Comments

A prime factor of 2^n+1 is called primitive if it does not divide 2^r+1 for any r<n. See A086257 for the number of primitive prime factors in 2^n+1. It is known that a(8) = 194.

Next term is > 666. - David Wasserman, Feb 25 2005

References

J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Links

Table of n, a(n) for n=1..12.

J. Brillhart et al., Factorizations of b^n +- 1 Available on-line

Example

a(2) = 14 because 2^14+1 = 5*29*113 and 29 and 113 do not divide 2^r+1 for r < 14.

Crossrefs

Cf. A086252, A086257.

Sequence in context: A242395 A112772 A155505 * A372008 A063799 A086451

Adjacent sequences: A086255 A086256 A086257 * A086259 A086260 A086261

Keyword

nonn,hard,more

Author

T. D. Noe, Jul 14 2003

Extensions

More terms from David Wasserman, Feb 25 2005

a(11) from D. S. McNeil, Dec 19 2010

a(12) from Amiram Eldar, Oct 12 2019

Status

approved