A177082 - OEIS

%I #15 Jan 14 2020 19:27:38

%S 6,32,90,208,390,672,1050,1568,2286,3160,4290,5664,7254,9128,11370,

%T 14016,16966,20376,24206,28400,33138,38368,44206,50784,57950,65624,

%U 73926,82768,92278,103080,114638,127104,140250,154632,169750,185904,203130,221312,240630

%N a(n) = 2*n*A071148(n).

%C a(n) is the sum of all elements of the n X n matrix M(i,j) = prime(i+1)+prime(j+1).

%C [For n<= 23, only five matrices (with n=1, n=2, n=3, n=5 and n=7) contain all the even numbers starting from 6 and ending with 2*prime(n+1), the maximum element. If the prime gap prime(n+1)-prime(n) is larger than 2, the even term 2*prime(n+1)-2 is missing in the matrix; the difference equal 2 between prime(n) and prime(n-1) is not a sufficient condition to have a complete set of even numbers in the range 6 .. 2*prime(n+1) in the matrix.]

%H Andrew Howroyd, <a href="/A177082/b177082.txt">Table of n, a(n) for n = 1..1000</a>

%o (Sage) A177082 = lambda n: 2*n*(sum(primes_first_n(n+1))-2) # _D. S. McNeil_, Dec 18 2010

%o (PARI) seq(n)={2*Vec(deriv((Ser(primes(n+1))-2)/(1-x)))} \\ _Andrew Howroyd_, Jan 14 2020

%Y Cf. A071148, A167214.

%K nonn

%O 1,1

%A _Giacomo Fecondo_, Dec 09 2010

%E Terms a(25) and beyond from _Andrew Howroyd_, Jan 14 2020