A244646 Decimal expansion of the sum of the reciprocals of the 9-gonal (or enneagonal or nonagonal) numbers (A001106).

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

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Ravi P. Agarwal, Pythagoreans Figurative Numbers: The Beginning of Number Theory and Summation of Series, Journal of Applied Mathematics and Physics, Vol.9, No.8 (2021), pp. 2038-2113. See p. 2076.

Wikipedia, Polygonal number.

Formula

Equals Sum_{n>=1} 2/(7n^2 - 5n).

Equals (2*log(14) + 4*(cos(Pi/7)*log(cos(3*Pi/14)) + log(sin(Pi/7))*sin(Pi/14) - log(cos(Pi/14)) * sin(3*Pi/14)) + Pi*tan(3*Pi/14))/5. - Vaclav Kotesovec, Jul 04 2014

Equals 14/25 - (2/5)*(gamma + psi(-5/7)), where gamma is Euler's constant (A001620) and psi(x) is the digamma function (Agarwal, 2021), psi(-5/7) = psi(2/7)+7/5 = -2.285517..., see A354628. - Amiram Eldar, Nov 12 2021

Example

1.2433209261537129892066077396310142821358441010300996244152817525...

Mathematica

RealDigits[ Sum[2/(7n^2 - 5n), {n, 1 , Infinity}], 10, 111][[1]]

Crossrefs

Cf. A000038, A001106, A013661, A001620, A244639, A244644, A244645, A244647, A244648, A244649.

Sequence in context: A216842 A099066 A021415 * A308182 A220080 A343766

Adjacent sequences: A244643 A244644 A244645 * A244647 A244648 A244649

Keyword

nonn,cons,easy

Author

Robert G. Wilson v, Jul 03 2014

Status

approved