Search: id:A095117
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%I A095117
%S A095117 0,1,3,5,6,8,9,11,12,13,14,16,17,19,20,21,22,24,25,27,28,29,30,32,33,34,
%T A095117 35,36,37,39,40,42,43,44,45,46,47,49,50,51,52,54,55,57,58,59,60,62,63,
%U A095117 64,65,66,67,69,70,71,72,73,74,76,77,79,80,81,82,83,84,86,87,88,89,91
%N A095117 Pi(n)+n, where pi(n) = A000720(n) is the number of primes <= n.
%C A095117 Comments from Paolo P. Lava (ppl(AT)spl.at), Jun 05 2008 (Start): Consider 
               the sequence of natural numbers A000027: 1,2,3,4,5,6,7,8....
%C A095117 Taking Pn=n-th prime, apply the following sieve:
%C A095117 Delete the number in position P1=2 -> 2 and compact:
%C A095117 1,3,4,5,6,7,8....
%C A095117 Then delete the number in position P2=3 ->4 and compact:
%C A095117 1,3,5,6,7,8,9,10,11..
%C A095117 Then delete the number in position P3=5 ->7 and compact:
%C A095117 1,3,5,6,8,9,10,11
%C A095117 and so on. (End)
%C A095117 Positions of first occurrences of n in A165634: A165634(a(n))=n for n>
               0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 
               23 2009]
%H A095117 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%F A095117 a(0) = 0, a(1) = 1, a(2) = 3; for n>2 a(n) = a(n-1) + (if n is prime 
               then 1, else 2). - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 22 
               2007; corrected by Philippe Lallouet (philip.lallouet(AT)orange.fr), 
               Aug 04 2008
%p A095117 with(numtheory): seq(n+pi(n),n=1..90); - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               May 02 2007
%t A095117 Table[ PrimePi@n + n, {n, 0, 71}] (* Or *) - Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Apr 22 2007
%t A095117 a[0] = 0; a[n_] := a[n] = a[n - 1] + If[PrimeQ@n, 2, 1]; Table[a@n, {n, 
               0, 71}] - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 22 2007
%Y A095117 Complement of A095116.
%Y A095117 Sequence in context: A002150 A153264 A133561 this_sequence A089585 A121506 
               A114119
%Y A095117 Adjacent sequences: A095114 A095115 A095116 this_sequence A095118 A095119 
               A095120
%K A095117 easy,nonn
%O A095117 0,3
%A A095117 Dean Hickerson (dean.hickerson(AT)yahoo.com), following a suggestion 
               of Leroy Quet May 28 2004
%E A095117 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 02 2008 at 
               the suggestion of R. J. Mathar

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