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A007917 Version 1 of the "previous prime" function: largest prime <= n. 101
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; text; internal format)
OFFSET

2,1

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 Elemer, Jun 22 2000

Also largest prime among terms of (n+1)st row of Pascal's triangle. - Jud McCranie, Jan 17 2000

Also largest integer k such that A000203(k) <= n+1. - Benoit Cloitre, Mar 17 2002. - Corrected by Antti Karttunen, Nov 07 2017

Also largest prime factor of A061355(n) (denominator of Sum_{k=0..n} 1/k!). - Jonathan Sondow, Jan 09 2005

Also prime(pi(x)) where pi(x) is the prime counting function = number of primes <= x. - Cino Hilliard, May 03 2005

Also largest prime factor, occurring to the power p, in denominator of Sum_{k=1..n} 1/k^p, for any positive integer p. - M. F. Hasler, Nov 10 2006

For n > 10, these values are close to the most negative eigenvalues of A191898 (conjecture). - Mats Granvik, Nov 04 2011

REFERENCES

K. Atanassov, On the 37th and the 38th 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.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 2..10000

Marc Deleglise and Jean-Louis Nicolas, Maximal product of primes whose sum is bounded, arXiv preprint arXiv:1207.0603 [math.NT], 2012. See Fig. 1. - From N. J. A. Sloane, Dec 17 2012

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. F. Smarandache, Only Problems, Not Solutions!.

Eric Weisstein's World of Mathematics, Previous Prime

FORMULA

Equals A006530(A000142(n)). - Jonathan Sondow, Jan 09 2005

Equals A006530(A056040(n)). - Peter Luschny, Mar 04 2011

a(n) = A000040(A049084(A007918(n)) + 1 - A010051(n)). - Reinhard Zumkeller, Jul 26 2012

From Wesley Ivan Hurt, May 22 2013: (Start)

omega( Product_{i=2..n} a(i) ) = pi(n).

Omega( Product_{i=2..n} a(i) ) = n - 1. (End)

For n >= 2, a(A000203(n)) = A070801(n). - Antti Karttunen, Nov 07 2017

MAPLE

A007917 := n-> prevprime(n+1);

MATHEMATICA

Table[Prime[PrimePi[n]], {n, 2, 70}] (* Stefan Steinerberger, Apr 06 2006 *)

NextPrime[Range[3, 80], -1] (* Harvey P. Dale, Jan 23 2011 *)

PROG

(PARI) a=precprime \\ In older versions, use a(n)=precprime(n)

\\ Charles R Greathouse IV, Jun 15 2011

(Haskell)

a007917 n = if a010051' n == 1 then n else a007917 (n-1)

-- Reinhard Zumkeller, May 01 2013, Jul 26 2012

(MAGMA) [NthPrime(#PrimesUpTo(n)): n in [2..100]]; // Vincenzo Librandi, Nov 25 2015

CROSSREFS

Cf. A000040, A000203, A005145, A007918, A070801, A113523, A151799, A179278.

Sequence in context: A284412 A136548 * A151799 A093841 A281354 A283313

Adjacent sequences:  A007914 A007915 A007916 * A007918 A007919 A007920

KEYWORD

nonn,easy,nice

AUTHOR

R. Muller

EXTENSIONS

Edited by N. J. A. Sloane, Apr 06 2008

STATUS

approved

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Last modified February 18 23:26 EST 2018. Contains 299330 sequences. (Running on oeis4.)