A177082 a(n) = 2*n*A071148(n).

6, 32, 90, 208, 390, 672, 1050, 1568, 2286, 3160, 4290, 5664, 7254, 9128, 11370, 14016, 16966, 20376, 24206, 28400, 33138, 38368, 44206, 50784, 57950, 65624, 73926, 82768, 92278, 103080, 114638, 127104, 140250, 154632, 169750, 185904, 203130, 221312, 240630

Offset: 1

Author

Giacomo Fecondo, Dec 09 2010

Keywords

• nonn

Comments

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

[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.]

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A071148, A167214.

Programs

PARI

seq(n)={2*Vec(deriv((Ser(primes(n+1))-2)/(1-x)))} \\ Andrew Howroyd, Jan 14 2020

Sage

A177082 = lambda n: 2*n*(sum(primes_first_n(n+1))-2) # D. S. McNeil, Dec 18 2010

Extensions

Terms a(25) and beyond from Andrew Howroyd, Jan 14 2020