A213926 -id:A213926 - cp's OEIS frontend

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

Altug Alkan, Sep 09 2015

nonn

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

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

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

Cf. A000040, A011757, A213926.

[NthPrime(n^2) div NthPrime(n): n in [1..70]]; // Vincenzo Librandi, May 24 2019

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

a(n) = floor(prime(n^2) / prime(n));
vector(70, n, a(n))

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

[floor(nth_prime(n^2)/nth_prime(n)) for n in (1..70)] # G. C. Greubel, May 24 2019

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

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

A214612 prime(n^3) - prime(n).

Original entry on oeis.org

0, 16, 98, 304, 680, 1308, 2292, 3652, 5496, 7890, 10926, 14716, 19362, 24766, 31272, 38820, 47598, 57498, 68964, 81728, 96064, 112212, 129990, 149628, 171432, 194942, 220758, 248744, 279322, 312470, 347580, 385962, 427032, 470794, 517404, 567720, 620374

Offset: 1

Jonathan Vos Post, Mar 06 2013

This is to exponent 3 as A213926 is to exponent 2.

			a(1) = prime(1^3) - prime(1) = 2-2 = 0.
a(2) = prime(2^3) - prime(2) = 19-3 = 16.
a(3) = prime(3^3) - prime(3) = 103-5 = 98.

Cf. A000040, A001223, A031131, A031165-A031172, A072473, A092504, A213926.

Table[Prime[n^3] - Prime[n], {n, 50}] (* T. D. Noe, Mar 07 2013 *)

cp's OEIS Frontend

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

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