OFFSET
0,2
COMMENTS
Starting from a(3) = 4, this constant represents the sum of the reciprocals of the sequence M(n) of magic constants for n X n magic squares (numbered 1 through n^2), considering n >= 3.
Sum_{n >= 3} 1/M(n) = 1/15 + 1/34 + 1/65 + 1/111 + 1/175 + 1/260 + ... = 1.34373197104801967... - 6/5 = 0.14373197104801967...
LINKS
Eric Weisstein's World of Mathematics, Magic Constant.
FORMULA
Equals Sum_{k>=3} 1/A006003(k).
Equals H(2 - I) + H(2 + I) - 3, where H(x) = Integral_{t=0..1} (1 - t^x)/(1 - t) dt is the function that interpolates the harmonic numbers and I is the imaginary unit. - Stefano Spezia, Dec 26 2020
EXAMPLE
0.143731971048019675756781145608626...
MATHEMATICA
RealDigits[Re @ Sum[2/(n*(n^2 + 1)), {n, 3, Infinity}], 10, 100][[1]] (* Amiram Eldar, Dec 26 2020 *)
PROG
(PARI) sumpos(n=3, 2/(n*(n^2 + 1))) \\ Michel Marcus, Dec 26 2020
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Marco Ripà, Dec 26 2020
STATUS
approved