This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A246010 #16 Sep 08 2022 08:46:09 %S A246010 5,11,31,61,151,211,361,451,661,1051,1201,1711,2101,2311,2761,3511, %T A246010 4351,4651,5611,6301,6661,7801,8611,9901,11761,12751,13261,14311, %U A246010 14851,15961,20161,21451,23461,24151,27751,28501,30811,33211 %N A246010 a(n) = floor(5*prime(n)^2 / 4). %C A246010 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. %H A246010 Freimut Marschner, <a href="/A246010/b246010.txt">Table of n, a(n) for n = 1..1044</a> %F A246010 a(n) = A032527(A000040(n)). - _Michel Marcus_, Sep 30 2014 %e A246010 a(4) = floor(5*7^2 / 4) = floor(61.25) = 61. %t A246010 Floor[(5*Prime[Range[40]]^2)/4] (* _Harvey P. Dale_, Sep 15 2019 *) %o A246010 (PARI) %o A246010 vector(100,n,floor(5*prime(n)^2/4)) \\ _Derek Orr_, Sep 30 2014 %o A246010 (Magma) [Floor(5*NthPrime(n)^2 / 4): n in [1..40]]; // _Vincenzo Librandi_, Oct 21 2014 %Y A246010 Cf. A032527 (the concentric pentagonal numbers: floor( 5*n^2 / 4)). %K A246010 nonn,easy %O A246010 1,1 %A A246010 _Freimut Marschner_, Sep 28 2014