A246010 - OEIS

A246010

a(n) = floor(5*prime(n)^2 / 4).

5, 11, 31, 61, 151, 211, 361, 451, 661, 1051, 1201, 1711, 2101, 2311, 2761, 3511, 4351, 4651, 5611, 6301, 6661, 7801, 8611, 9901, 11761, 12751, 13261, 14311, 14851, 15961, 20161, 21451, 23461, 24151, 27751, 28501, 30811, 33211

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OFFSET

1,1

COMMENTS

Let f(x) = -x^2 + b*x + b^2 be a polynomial function with b = prime(n), n >= 1, then the vertex of the graph of f(x) is at the point (vx;f(vx)) = (b/2;5*b^2/4) with f’(vx) = -2*vx + b = 0. If b = n, n >= 0, then the sequence of the vertex of this polynomial is A032527, the concentric pentagonal numbers: floor( 5*n^2 / 4). So a(n) = floor( 5*prime(n)^2 / 4), n >= 1 is a subsequence of A032527.

LINKS

Freimut Marschner, Table of n, a(n) for n = 1..1044

FORMULA

a(n) = A032527(A000040(n)). - Michel Marcus, Sep 30 2014

EXAMPLE

a(4) = floor(5*7^2 / 4) = floor(61.25) = 61.

MATHEMATICA

Floor[(5*Prime[Range[40]]^2)/4] (* Harvey P. Dale, Sep 15 2019 *)

PROG

(PARI)

vector(100, n, floor(5*prime(n)^2/4)) \\ Derek Orr, Sep 30 2014

(Magma) [Floor(5*NthPrime(n)^2 / 4): n in [1..40]]; // Vincenzo Librandi, Oct 21 2014