A248911 a(n) = floor( prime(n) - (n+1)*log(n) ).

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, 16, 18, 15, 21, 18, 19, 21, 20, 21, 23, 20, 25, 22, 21, 19, 26, 33, 32, 29, 28, 29, 26, 31, 32, 33, 34, 31, 32, 31, 28, 32, 41, 40, 37, 36, 45, 45, 50, 47, 46, 46

Offset: 1

Author

Michel Lagneau, Oct 16 2014

Keywords

• nonn

Comments

The function log gives the natural logarithm (to base e).

See A059111 for the sequence a(n) = floor(prime(n)-n*log(n)).

Examples

			a(8) = 0 because floor(prime(8)-(8+1)*log(8)) = floor(19 -9*2.07944154...) = floor(.28502612...) = 0.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A059111, A059112.

Programs

Magma

[Floor(NthPrime(n)-(n+1)*Log(n)): n in [1..80]]; // Vincenzo Librandi, Oct 16 2014

Maple

with(numtheory):
for n from 1 to 200 do:
  p:=floor(evalf(ithprime(n)-(n+1)*ln(n))): printf(`%d, `,p):
od:

Mathematica

Table[Floor[Prime[n]-(n+1)Log[n]], {n, 100}]