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A082449
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Let f(p) = greatest prime divisor of p-1. Sequence gives smallest prime which takes at least n steps to reach 2 when f is iterated.
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3
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2, 3, 7, 23, 47, 283, 719, 1439, 2879, 34549, 138197, 1266767, 14619833, 36449279, 377982107, 1432349099, 22111003847
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| There is a remarkable and unexplained agreement: if 3 and 7 are replaced by 11 and 14619833 is replaced by 14920303, the result is sequence A056637 (least prime of class n-, according to the Erdos-Selfridge classification of primes).
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REFERENCES
| Steven G. Johnson, Postings to Number Theory List, Apr 23 and Apr 25, 2003.
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EXAMPLE
| a(2) = 7 since 7 -> 3 -> 2 takes two steps; for p = 2879, 8 steps are needed (2879 -> 1439 -> 719 -> 359 -> 179 -> 89 -> 11 -> 5 -> 2), so a(8) = 2879; smaller primes require less than 2 resp. 8 steps.
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CROSSREFS
| Cf. A006530, A023503, A083647, A056637, A083647.
Sequence in context: A106865 A000057 A037231 * A129741 A006720 A084710
Adjacent sequences: A082446 A082447 A082448 * A082450 A082451 A082452
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KEYWORD
| nonn,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 25 2003
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EXTENSIONS
| Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 01 2003
a(16) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Nov 17 2008
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