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

Author

N. J. A. Sloane, May 13 2007

Keywords

• nonn

Comments

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

Examples

			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], ...
		

Links

• 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.

Crossrefs

Cf. A002450, A129733.

Extensions

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