A129735 List of primitive prime divisors of the numbers (4^n-1)/3 (A002450) in their order of occurrence.

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

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