A078746 - OEIS

%I #19 Sep 08 2022 08:45:08

%S 2,11,41,97,179,283,439,617,829,1087,1381,1697,2081,2467,2909,3433,

%T 3929,4517,5119,5801,6481,7237,8059,8863,9739,10663,11701,12659,13729,

%U 14867,15973,17239,18443,19843,21179,22549,23971,25541,27043,28657

%N a(n) = prime(2*n*(n+1)+1).

%C Central elements of odd-length rows of the triangle of primes:

%C .           2,

%C .         3,   5,

%C .       7,  11, 13,

%C .     17, 19, 23, 29,

%C .   31, 37, 41, 43, 47,

%C . 53, 59, 61, 67, 71, 73, etc.

%C The sum of the reciprocals of the terms converges by comparison with sum_{n>=1} 1/n^2, since 1/a(n) < 1/(2n(n+1)+1) < 1/n^2. The limit is about 0.6471.

%H Vincenzo Librandi, <a href="/A078746/b078746.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A000040(A001844(n)). - _David James Sycamore_, Aug 01 2018

%t Table[Prime[2n(n+1)+1],{n,0,40}] (* _Harvey P. Dale_, May 02 2012 *)

%o (PARI) triprimes(n) = { sr = 0; for(j= 1,n, x = 2*j*(j-1) + 1; z = prime(x); sr+=1.0/z; print1(z" "); ); print(); print(sr); }

%o (Magma) [NthPrime(2*n*(n + 1)+1): n in [0..50]]; // _Vincenzo Librandi_, Jun 08 2016

%Y Cf. A000040, A078721, A001844.

%K nonn,easy

%O 0,1

%A _Cino Hilliard_, Dec 21 2002

%E Edited by _Dean Hickerson_, Dec 23 2002