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Search: id:A095117
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| A095117 |
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Pi(n)+n, where pi(n) = A000720(n) is the number of primes <= n. |
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+0
5
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| 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, 35, 36, 37, 39, 40, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 91
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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....
Taking Pn=n-th prime, apply the following sieve:
Delete the number in position P1=2 -> 2 and compact:
1,3,4,5,6,7,8....
Then delete the number in position P2=3 ->4 and compact:
1,3,5,6,7,8,9,10,11..
Then delete the number in position P3=5 ->7 and compact:
1,3,5,6,8,9,10,11
and so on. (End)
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]
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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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
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MAPLE
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with(numtheory): seq(n+pi(n), n=1..90); - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 02 2007
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MATHEMATICA
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Table[ PrimePi@n + n, {n, 0, 71}] (* Or *) - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 22 2007
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
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CROSSREFS
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Complement of A095116.
Sequence in context: A002150 A153264 A133561 this_sequence A089585 A121506 A114119
Adjacent sequences: A095114 A095115 A095116 this_sequence A095118 A095119 A095120
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KEYWORD
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easy,nonn
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AUTHOR
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Dean Hickerson (dean.hickerson(AT)yahoo.com), following a suggestion of Leroy Quet May 28 2004
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EXTENSIONS
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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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