login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A129735 List of primitive prime divisors of the numbers (4^n-1)/3 (A002450) in their order of occurrence. 2
5, 3, 7, 17, 11, 31, 13, 43, 127, 257, 19, 73, 41, 23, 89, 683, 241, 2731, 8191, 29, 113, 151, 331, 65537, 43691, 131071, 37, 109, 174763, 524287, 61681, 337, 5419, 397, 2113, 47, 178481, 2796203, 97, 673, 251, 601, 1801, 4051, 53, 157, 1613, 87211, 262657, 15790321, 59, 233, 1103, 2089, 3033169, 61, 1321, 715827883, 2147483647 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Read A002450 term-by-term, factorize each term, write down any primes not seen before in increasing order for each term.

LINKS

Table of n, a(n) for n=1..59.

James R. Buddenhagen, List giving n followed by primitive prime divisors of (4^n-1)/3 for n=1..70

G. Everest, S. Stevens, D. Tamsett and T. Ward, Primes Generated by Recurrence Sequences, 2006.

G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.

Wikipedia, Zsigmondy's theorem

K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math., 3 (1892), 265-284.

EXAMPLE

The primes grouped according to successive terms of A002450, courtesy of James R. Buddenhagen:

[5], [3, 7], [17], [11, 31], [13], [43, 127], [257], [19, 73], [41], [23, 89, 683], [241], [2731, 8191], [29, 113], [151, 331], [65537], [43691, 131071], [37, 109], [174763, 524287], [61681], [337, 5419], [397, 2113], [47, 178481, 2796203], [97, 673], [251, 601, 1801, 4051], [53, 157, 1613], [87211, 262657], [15790321], [59, 233, 1103, 2089, 3033169], [61, 1321], [715827883, 2147483647], ...

CROSSREFS

Cf. A002450, A129733.

Sequence in context: A030669 A030679 A077891 * A300502 A248257 A019663

Adjacent sequences:  A129732 A129733 A129734 * A129736 A129737 A129738

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 13 2007

EXTENSIONS

Order of terms corrected by James R. Buddenhagen, Jul 23 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)