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) ~ 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
KEYWORD
nonn
AUTHOR
Altug Alkan, Sep 09 2015
STATUS
approved