A001729 - OEIS

A001729

List of numbers whose digits contain no loops (version 1).

1, 2, 3, 4, 5, 7, 11, 12, 13, 14, 15, 17, 21, 22, 23, 24, 25, 27, 31, 32, 33, 34, 35, 37, 41, 42, 43, 44, 45, 47, 51, 52, 53, 54, 55, 57, 71, 72, 73, 74, 75, 77, 111, 112, 113, 114, 115, 117, 121, 122, 123, 124, 125, 127, 131, 132, 133, 134, 135, 137, 141, 142

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The digits 0, 6, 8 and 9 contain loops, but 1, 2, 3, 4 (written in "open" style), 5 and 7 do not.

LINKS

T. D. Noe, 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.

Index entries for 10-automatic sequences.

FORMULA

Sum_{n>=1} 1/a(n) = 5.427161361994446672956800952211331066904630376796246807177210248900020978222... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 15 2024

MATHEMATICA

Select[Range[150], Intersection[{0, 6, 8, 9}, Union[IntegerDigits[#]]] == {} &] (* T. D. Noe, Aug 10 2012 *)

FromDigits/@Flatten[Table[Tuples[{1, 2, 3, 4, 5, 7}, n], {n, 3}], 1] (* Harvey P. Dale, Feb 01 2017 *)

CROSSREFS

Cf. A001742 (version 2).

Sequence in context: A345663 A191864 A180348 * A001087 A191876 A234719

Adjacent sequences: A001726 A001727 A001728 * A001730 A001731 A001732

KEYWORD

base,nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Missing 42 and 44 added by T. D. Noe, Aug 10 2012

STATUS

approved