login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057934 Number of prime factors of 10^n + 1 (counted with multiplicity). 14
1, 1, 3, 2, 2, 2, 2, 2, 5, 3, 5, 3, 3, 4, 7, 5, 4, 3, 2, 4, 8, 4, 5, 3, 5, 3, 7, 4, 3, 7, 2, 4, 9, 4, 5, 6, 4, 3, 10, 4, 3, 7, 4, 4, 12, 4, 4, 9, 4, 7, 8, 4, 2, 6, 10, 5, 6, 5, 4, 6, 3, 3, 12, 3, 6, 8, 2, 4, 10, 11, 3, 5, 4, 7, 11, 6, 12, 7, 4, 9, 11, 3, 7, 8, 8, 3, 8, 4, 4, 11, 6, 4, 8, 4, 6, 8, 4, 5, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

2^(a(2n)-1)-1 predicts the number of pair-solutions of even length L for AB = A^2 + B^2. For instance, with length 18 we have 10^18 + 1 = 101*9901*999999000001 or 3 divisors F which when put into the Mersenne formula 2^(F-1)-1 yields 3 pairs (see reference 'Puzzle 104' for details).

LINKS

Ray Chandler, Table of n, a(n) for n = 1..310 (from Kamada link)

Makoto Kamada, Factorizations of 100...001.

Carlos Rivera, Puzzle 104, The Prime Puzzles & Problems Connection.

S. S. Wagstaff, Jr., Main Tables from the Cunningham Project.

S. S. Wagstaff, Jr., The Cunningham Project

FORMULA

a(n) = A057951(2n) - A057951(n). - T. D. Noe, Jun 19 2003

PROG

(PARI) a(n)=bigomega(10^n+1) \\ Charles R Greathouse IV, Sep 14 2015

CROSSREFS

Cf. A003021, A001271, A046053, A057935-A057941, A054992, A001562, A057951.

Sequence in context: A174550 A119704 A104223 * A058758 A122396 A272893

Adjacent sequences:  A057931 A057932 A057933 * A057935 A057936 A057937

KEYWORD

nonn

AUTHOR

Patrick De Geest, Oct 15 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 9 10:52 EDT 2020. Contains 333348 sequences. (Running on oeis4.)