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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
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.
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
Sequence in context: A030669 A030679 A077891 * A300502 A248257 A019663
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 13 2007
EXTENSIONS
Order of terms corrected by James R. Buddenhagen, Jul 23 2015
STATUS
approved

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)