A340012 Decimal expansion of Sum_{n>=3} 2/(n*(n^2 + 1)).

1, 4, 3, 7, 3, 1, 9, 7, 1, 0, 4, 8, 0, 1, 9, 6, 7, 5, 7, 5, 6, 7, 8, 1, 1, 4, 5, 6, 0, 8, 6, 2, 6, 3, 0, 7, 0, 3, 6, 8, 4, 4, 6, 1, 5, 4, 0, 6, 9, 3, 0, 4, 4, 4, 0, 7, 7, 5, 1, 3, 9, 1, 8, 0, 0, 7, 5, 4, 5, 6, 8, 3, 0, 7, 3, 8, 9, 0, 6, 4, 8, 6, 4, 0, 8, 3

Offset: 0

Author

Marco Ripà, Dec 26 2020

Keywords

• cons
• nonn

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...

Examples

			0.143731971048019675756781145608626...
		

Links

• Eric Weisstein's World of Mathematics, Magic Constant.

Crossrefs

Cf. A006003, A340012.

Programs

Mathematica

RealDigits[Re @ Sum[2/(n*(n^2 + 1)), {n, 3, Infinity}], 10, 100][[1]] (* Amiram Eldar, Dec 26 2020 *)

PARI

sumpos(n=3, 2/(n*(n^2 + 1))) \\ Michel Marcus, Dec 26 2020

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