A086252 a(n) is the smallest k such that 2^k-1 has n primitive prime factors.

2, 11, 29, 92, 113, 223, 295, 333, 397, 1076

Offset

1,1

Comments

A prime factor of 2^n-1 is called primitive if it does not divide 2^r-1 for any r<n. Equivalently, p is a primitive prime factor of 2^n-1 if ord(2,p)=n. See A086251 for the number of primitive prime factors in 2^n-1.

No more terms < 673. (2^673-1 is the first that is not completely factored in the linked reference.) - David Wasserman, Feb 22 2005

2^1207-1 is now the first not completely factored number of the form 2^k-1. - Hugo Pfoertner, Aug 06 2019

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..10.

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

factordb.com, Factors of 2^1076-1.

factordb.com, Status of 2^n-1 for n>1200.

Example

a(2) = 11 because 2^11-1 = 23*89, both 23 and 89 have order 11 and the numbers 2^r-1 have only 0 or 1 primitive prime factors.

Crossrefs

Cf. A086251.

Sequence in context: A154251 A092275 A295841 * A106926 A220095 A133558

Adjacent sequences: A086249 A086250 A086251 * A086253 A086254 A086255

Keyword

hard,more,nonn

Author

T. D. Noe, Jul 14 2003

Extensions

More terms from David Wasserman, Feb 22 2005

a(10) from Hugo Pfoertner, Aug 06 2019

Status

approved