cp's OEIS Frontend

A037168 a(n) = 2*prime(n) - 2.

%I A037168 #33 Aug 02 2023 18:56:13
%S A037168 2,4,8,12,20,24,32,36,44,56,60,72,80,84,92,104,116,120,132,140,144,
%T A037168 156,164,176,192,200,204,212,216,224,252,260,272,276,296,300,312,324,
%U A037168 332,344,356,360,380,384,392,396,420,444,452,456
%N A037168 a(n) = 2*prime(n) - 2.
%C A037168 Original definition: Prime(n)+ Sum(prime(n-z) mod prime(n-z-1)); z=0,1...n-2 ; with offset 2.
%C A037168 Since prime(n+1) < 2*prime(n) for all n, the "mod" in the sum is equivalent to "-", making it telescopic and equal to prime(n)-2. - _M. F. Hasler_, Jun 29 2013
%H A037168 Vincenzo Librandi, <a href="/A037168/b037168.txt">Table of n, a(n) for n = 1..1000</a>
%H A037168 Barry Brent, <a href="https://arxiv.org/abs/2212.12515">On the constant terms of certain meromorphic modular forms for Hecke groups</a>, arXiv:2212.12515 [math.NT], 2022.
%H A037168 Barry Brent, <a href="https://doi.org/10.20944/preprints202306.1164.v6">On the Constant Terms of Certain Laurent Series</a>, Preprints (2023) 2023061164.
%F A037168 a(n) = 2 * prime(n) - 2 =  2 * phi(prime(n)). - _Alonso del Arte_, Jun 30 2013
%F A037168 a(n) = 2 * A006093(n). - _Ray Chandler_, Jun 30 2013
%F A037168 a(n) = A000010(A000040(n)) - A023900(A000040(n)). - _Torlach Rush_, Mar 11 2018
%e A037168 a(3) = 8 since the third prime is 5 and 2 * 5 - 2 = 8.
%t A037168 2Prime[Range[50]] - 2 (* _Alonso del Arte_, Jun 30 2013 *)
%o A037168 (PARI) A037168 = n->prime(n)*2-2  \\ _M. F. Hasler_, Jun 29 2013
%o A037168 (Magma) [2*p-2: p in PrimesUpTo(300)]; // _Vincenzo Librandi_, Mar 19 2014
%Y A037168 Cf. A000010, A000040, A006093, A023900.
%K A037168 nonn,easy
%O A037168 1,1
%A A037168 Armand Turpel (armandt(AT)unforgettable.com)
%E A037168 Definition simplified and extended to n=1, following a suggestion from _Alonso del Arte_, by _M. F. Hasler_, Jun 29 2013