A138563 Beastly fax numbers: numbers containing the fax number of the Beast (667, one more than its regular number) in their decimal expansion.

667, 1667, 2667, 3667, 4667, 5667, 6667, 6670, 6671, 6672, 6673, 6674, 6675, 6676, 6677, 6678, 6679, 7667, 8667, 9667, 10667, 11667, 12667, 13667, 14667, 15667, 16667, 16670, 16671, 16672, 16673, 16674, 16675, 16676, 16677, 16678

Offset: 1

Author

N. J. A. Sloane, May 13 2007

Keywords

• nonn
• dumb
• easy
• base

Comments

The sum of the reciprocals of numbers not in this sequence is convergent. - Adam P. Goucher, Apr 27 2014

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..1000
• Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
• Margaret Wertheim and Neil Sloane, The Fax Numbers of the Beast, and Other Mathematical Sports: An Interview with Neil Sloane, Cabinet, Spring 2015.

Crossrefs

Cf. A051003.

Programs

Mathematica

Select[Range[20000], StringContainsQ[ToString[#], "667"] &] (* Amiram Eldar, Jun 28 2024 *)

Formula

a(n) ~ n. - Charles R Greathouse IV, Oct 25 2014

Sum_{k>=1, k is not a term} 1/k = 2301.846622336249707557560554200194249235044868457872023381489896767824372028... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Jun 28 2024