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A007917
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Version 1 of the "previous prime" function: largest prime <= n.
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60
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2, 3, 3, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 29, 29, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 41, 41, 43, 43, 43, 43, 47, 47, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 61, 61, 61, 61, 61, 61, 67, 67, 67, 67, 71, 71, 73, 73, 73, 73
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Version 2 of the "previous prime" function (see A151799) is "largest prime < n". This produces the same sequence of numerical values, except the offset (or indexing) starts at 3 instead of 2.
Maple's "prevprime" function uses version 2.
Also the largest prime dividing n! or LCM[1,..,n] - Labos E. (labos(AT)ana.sote.hu), Jun 22 2000
Also largest prime among terms of (n+1)st row of Pascal's triangle - Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Jan 17 2000.
Also largest integer k such that A000203(k)<=n+2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 17 2002
Also largest prime factor of A061355(n) (denominator of Sum_{k=0..n} 1/k!). - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 09 2005
Also prime(pi(x)) where pi(x) is the prime counting function = number of primes <= x. - Cino Hilliard (hillcino368(AT)gmail.com), May 03 2005
Also largest prime factor, occurring to the power p, in denominator of sum(1/k^p,k=1..n), for any positive integer p. - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 10 2006
For n>10, these values are close to the most negative eigenvalues of A191898 (conjecture). - Mats Granvik, Nov 04 2011
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REFERENCES
| K. Atanassov, On the 37-th and the 38-th Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5 (1999), No. 2, 83-85.
J. Castillo, Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 202-204.
F. Smarandache, Only Problems, not Solutions!, Xiquan Publ., Phoenix-Chicago, 1993.
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 2..10000
Hans Gunter, Puzzle 145. The Inferior Smarandache Prime Part and Superior Smarandache Prime Part functions; Solutions by Jean Marie Charrier, Teresinha DaCosta, Rene Blanch, Richard Kelley and Jim Howell.
M. L. Perez et al., eds., Smarandache Notions Journal
F. Smarandache, Only Problems, Not Solutions!.
Eric Weisstein's World of Mathematics, Previous Prime
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FORMULA
| Equals A006530(A000142(n)). - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jan 09 2005
Equals A006530(A056040(n)). - Peter Luschny, Mar 04 2011.
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MAPLE
| A007917 := n-> prevprime(n+1);
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MATHEMATICA
| Table[Prime[PrimePi[n]], {n, 2, 70}] (* Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 06 2006 *)
NextPrime[Range[3, 80], -1] (* From Harvey P. Dale, Jan 23 2011 *)
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PROG
| (PARI) a=precprime \\ In older versions, use a(n)=precprime(n)
\\ Charles R Greathouse IV, Jun 15 2011
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CROSSREFS
| Cf. A000040, A007918, A151799, A005145.
Cf. A179278, A113523.
Sequence in context: A093074 A136548 * A151799 A093841 A091937 A113637
Adjacent sequences: A007914 A007915 A007916 * A007918 A007919 A007920
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KEYWORD
| nonn,easy,nice
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AUTHOR
| R. Muller
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 06 2008
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