A160502 Decimal expansion of the (finite) value of Sum_{ k >= 1, k has only a single zero digit in base 2 } 1/k.

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

Offset: 1

Author

Robert G. Wilson v, May 15 2009

Keywords

• base
• cons
• nonn

Comments

The sum of 1/n where n has a single 0 in base 2.

Examples

			1.4625907350443646995461454467205346210747448647488211093642006243545229...
		

Links

• Robert Baillie, Summing The Curious Series Of Kempner And Irwin, arXiv:0806.4410 [math.CA], 2008-2015.

Crossrefs

Cf. A030130 (numbers with a single zero in base 2), A140502.

Programs

Mathematica

RealDigits[ N[ Sum[1/(2^n - 1 - 2^k), {n, 2, 400}, {k, 0, n - 2}], 111]][[1]]
(* first install irwinSums.m, see reference, then *) First@ RealDigits@ iSum[0, 1, 111, 2] (* Robert G. Wilson v, Aug 03 2010 *)

Formula

Equals Sum_{n>=2} Sum_{k=0..n-2}, 1/(2^n - 1 - 2^k).