A261619 a(n) = floor(prime(n^2) / prime(n)).

1, 2, 4, 7, 8, 11, 13, 16, 18, 18, 21, 22, 24, 27, 30, 30, 31, 35, 36, 38, 42, 43, 45, 47, 47, 50, 53, 56, 59, 61, 59, 62, 63, 67, 66, 70, 72, 73, 76, 78, 80, 83, 83, 86, 89, 92, 92, 91, 94, 97, 100, 101, 105, 105, 107, 109, 111, 115, 117, 119

Offset

1,2

Comments

Inspired by A213926.

The reason of "/" operation between prime(n^2) and prime(n) is n^2 / n = n.

Sequence is not monotone: 61 = a(30) > a(31) = 59. In the first thousand terms there are 83 less than the preceding term; in the first ten thousand, 865. - Charles R Greathouse IV, Sep 12 2015

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = floor(A011757(n) / A000040(n)).

a(n) ~ n/(2 log^2 n). - Charles R Greathouse IV, Sep 12 2015

Example

For n=2, a(n) = floor(prime(n^2) / prime(n)) =  floor(7/3) = 2.

Mathematica

Table[Floor[Prime[n^2] / Prime[n]], {n, 1, 100}] (* Vincenzo Librandi, May 24 2019 *)

Prog

(PARI) a(n) = floor(prime(n^2) / prime(n));
vector(70, n, a(n))
(PARI) first(n)=my(v=List(), p, k); forprime(q=2, , if(issquare(k++), p=nextprime(p+1); listput(v, q\p); if(#v==n, return(Vec(v))))) \\ Charles R Greathouse IV, Sep 12 2015
(Magma) [NthPrime(n^2) div NthPrime(n): n in [1..70]]; // Vincenzo Librandi, May 24 2019
(Sage) [floor(nth_prime(n^2)/nth_prime(n)) for n in (1..70)] # G. C. Greubel, May 24 2019

Crossrefs

Cf. A000040, A011757, A213926.

Sequence in context: A187838 A106265 A187834 * A187575 A316326 A074204

Adjacent sequences: A261616 A261617 A261618 * A261620 A261621 A261622

Keyword

nonn

Author

Altug Alkan, Sep 09 2015

Status

approved