login
Compressed primes: a(n) is the nearest integer to prime(n)/log prime(n).
(Formerly M2272 N0898)
3

%I M2272 N0898 #25 Nov 30 2022 11:57:36

%S 3,3,3,4,5,5,6,6,7,9,9,10,11,11,12,13,14,15,16,17,17,18,19,20,21,22,

%T 22,23,23,24,26,27,28,28,30,30,31,32,33,34,35,35,36,37,37,38,39,41,42,

%U 42,43,44,44,45,46,47,48,48,49,50,50,52,54,54,54,55,57,58,59,60,60,61,62

%N Compressed primes: a(n) is the nearest integer to prime(n)/log prime(n).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Harry J. Smith, <a href="/A002036/b002036.txt">Table of n, a(n) for n = 1..1000</a>

%H M. Stein and S. M. Ulam, <a href="http://www.jstor.org/stable/2314055">An Observation on the Distribution of Primes</a>, Amer. Math. Monthly 74, 43-44, 1967.

%F a(n) = n - O(n/log n). - _Charles R Greathouse IV_, Nov 30 2022

%t Table[ Round[ Prime[n] / Log[ Prime[n]]], {n, 1, 75}]

%o (PARI) n=0; forprime (p=1, 9999, a=round(p/log(p)); write("b002036.txt", n++, " ", a); if (n>=1000, break)) \\ _Harry J. Smith_, Jun 16 2009

%Y Cf. A070944.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Robert G. Wilson v_, May 15 2002