A151799 - OEIS

%I #39 Nov 29 2022 08:40:19

%S 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,

%T 23,29,29,31,31,31,31,31,31,37,37,37,37,41,41,43,43,43,43,47,47,47,47,

%U 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

%N Version 2 of the "previous prime" function: largest prime < n.

%C Version 1 of the "previous prime" function is "largest prime <= n". This produces A007917, the same sequence of numerical values, except the offset (or indexing) starts at 2 instead of 3.

%C Maple's "prevprime" function uses version 2.

%C See A007917 for references and further information.

%H Daniel Forgues, <a href="/A151799/b151799.txt">Table of n, a(n) for n = 3..100000</a>

%F a(n) = A000040(A000720(n-1)). - _Enrique Pérez Herrero_, Jul 23 2011

%F a(n) = n + 1 - Sum_{k=1..n}( floor(k!^(n-1)/(n-1)!)-floor((k!^(n-1)-1)/(n-1)!) ). - _Anthony Browne_, May 17 2016

%F a(n) = A060265(floor(n/2)) for n >= 4. - _Georg Fischer_, Nov 29 2022

%p A151799:=n->prevprime(n): seq(A151799(n), n=3..100);

%t Table[NextPrime[n, -1], {n, 3, 77}] (* _Jean-François Alcover_, May 27 2011 *)

%o (Maxima) makelist(prev_prime(n), n, 3, 79); /* _Bruno Berselli_, May 20 2011 */

%o (Haskell)

%o a151799 = a007917 . (subtract 1)  -- _Reinhard Zumkeller_, Jul 26 2012

%o (PARI) a(n)=precprime(n-1) \\ _Charles R Greathouse IV_, Jul 12 2016

%o (Python)

%o from sympy import prevprime

%o def A151799(n):

%o     return prevprime(n) # _Chai Wah Wu_, Feb 28 2018

%Y Cf. A000040, A007917, A007918, A060265, A151800.

%K nonn,easy,nice

%O 3,1

%A _N. J. A. Sloane_, Jun 29 2009