Search: id:A038606
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%I A038606
%S A038606 1,5,12,31,69,181,443,1052,2701,6455,15928,40073,100362,251707,637235,
%T A038606 1617175,4124437,10553415,27066974,69709680,179992909,465769803,
%U A038606 1208198526,3140421716,8179002096,21338685407,55762149030,145935689361
%N A038606 Least k such that k-th prime > n * k.
%C A038606 Log(a(n)) =~ -1.295 + 0.964312n. - Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Jan 25 2002
%C A038606 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.
%C A038606 A090973(a(n)) = n+1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 16 2009]
%H A038606 Labos, E. <a href="a004648.gif">Graph of first 50000 terms</a>
%H A038606 Andrew R. Booker, <a href="http://primes.utm.edu/nthprime/">The Nth Prime 
               Page</a>
%F A038606 a(n) = pi(A038607(n)) = A000720(A038607(n)).
%t A038606 k = 1; Do[ While[ Floor[ Prime[k]/k] < n, k++ ]; Print[k]; k++, {n, 1, 
               30} ]
%Y A038606 Cf. A038607, A004648.
%Y A038606 Sequence in context: A015625 A038357 A090974 this_sequence A066280 A136113 
               A050189
%Y A038606 Adjacent sequences: A038603 A038604 A038605 this_sequence A038607 A038608 
               A038609
%K A038606 nonn
%O A038606 1,2
%A A038606 Vasiliy Danilov (danilovv(AT)usa.net) 1998 Jul
%E A038606 Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 25 2002
%E A038606 a(21)=179992909 corrected by Ray Chandler (rayjchandler(AT)sbcglobal.net), 
               Dec 01 2004

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