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

1,1

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.

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

Mathematica

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

Crossrefs

Cf. A051003.

Sequence in context: A326255 A326256 A210477 * A327908 A092797 A105212

Adjacent sequences: A138560 A138561 A138562 * A138564 A138565 A138566

Keyword

nonn,dumb,easy,base,changed

Author

N. J. A. Sloane, May 13 2007

Status

approved