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Search: id:A038606
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| A038606 |
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Least k such that k-th prime > n * k. |
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+0
4
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| 1, 5, 12, 31, 69, 181, 443, 1052, 2701, 6455, 15928, 40073, 100362, 251707, 637235, 1617175, 4124437, 10553415, 27066974, 69709680, 179992909, 465769803, 1208198526, 3140421716, 8179002096, 21338685407, 55762149030, 145935689361
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Log(a(n)) =~ -1.295 + 0.964312n. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 25 2002
Numbers n such that Prime(n) (mod n) begins the next cycle of terms in A004648. Generally Prime(i) (mod i) exceeds Prime(i-1) (mod i-1) but there are numerous times where for a short run Prime(i) (mod i) is minimally less than its predecessor. Here n is substantially less. See Labos's graph.
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LINKS
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Labos, E. Graph of first 50000 terms
Andrew R. Booker, The Nth Prime Page
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FORMULA
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a(n) = pi(A038607(n)) = A000720(A038607(n)).
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MATHEMATICA
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k = 1; Do[ While[ Floor[ Prime[k]/k] < n, k++ ]; Print[k]; k++, {n, 1, 30} ]
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CROSSREFS
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Cf. A038607, A004648.
Sequence in context: A015625 A038357 A090974 this_sequence A066280 A136113 A050189
Adjacent sequences: A038603 A038604 A038605 this_sequence A038607 A038608 A038609
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KEYWORD
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nonn
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AUTHOR
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Vasiliy Danilov (danilovv(AT)usa.net) 1998 Jul
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 25 2002
a(21)=179992909 corrected by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 01 2004
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