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%I #10 Sep 08 2022 08:46:10
%S 2,0,0,0,1,0,1,0,1,3,2,4,5,3,3,5,8,6,8,8,6,7,7,9,13,13,10,10,7,7,17,
%T 16,18,15,21,18,19,21,20,21,23,20,25,22,21,19,26,33,32,29,28,29,26,31,
%U 32,33,34,31,32,31,28,32,41,40,37,36,45,45,50,47,46,46
%N a(n) = floor( prime(n) - (n+1)*log(n) ).
%C The function log gives the natural logarithm (to base e).
%C See A059111 for the sequence a(n) = floor(prime(n)-n*log(n)).
%H Michel Lagneau, <a href="/A248911/b248911.txt">Table of n, a(n) for n = 1..10000</a>
%e a(8) = 0 because floor(prime(8)-(8+1)*log(8)) = floor(19 -9*2.07944154...) = floor(.28502612...) = 0.
%p with(numtheory):
%p for n from 1 to 200 do:
%p p:=floor(evalf(ithprime(n)-(n+1)*ln(n))): printf(`%d, `,p):
%p od:
%t Table[Floor[Prime[n]-(n+1)Log[n]], {n, 100}]
%o (Magma) [Floor(NthPrime(n)-(n+1)*Log(n)): n in [1..80]]; // _Vincenzo Librandi_, Oct 16 2014
%Y Cf. A000040, A059111, A059112.
%K nonn
%O 1,1
%A _Michel Lagneau_, Oct 16 2014