A261619 - OEIS

%I #47 Sep 08 2022 08:46:13

%S 1,2,4,7,8,11,13,16,18,18,21,22,24,27,30,30,31,35,36,38,42,43,45,47,

%T 47,50,53,56,59,61,59,62,63,67,66,70,72,73,76,78,80,83,83,86,89,92,92,

%U 91,94,97,100,101,105,105,107,109,111,115,117,119

%N a(n) = floor(prime(n^2) / prime(n)).

%C Inspired by A213926.

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

%C 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

%H Charles R Greathouse IV, <a href="/A261619/b261619.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) ~ n/(2 log^2 n). - _Charles R Greathouse IV_, Sep 12 2015

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

%t Table[Floor[Prime[n^2] / Prime[n]], {n, 1, 100}] (* _Vincenzo Librandi_, May 24 2019 *)

%o (PARI) a(n) = floor(prime(n^2) / prime(n));

%o vector(70, n, a(n))

%o (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

%o (Magma) [NthPrime(n^2) div NthPrime(n): n in [1..70]]; // _Vincenzo Librandi_, May 24 2019

%o (Sage) [floor(nth_prime(n^2)/nth_prime(n)) for n in (1..70)] # _G. C. Greubel_, May 24 2019

%Y Cf. A000040, A011757, A213926.

%K nonn

%O 1,2

%A _Altug Alkan_, Sep 09 2015