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

Offset: 1

Author

N. J. A. Sloane

Keywords

• base
• nonn
• easy

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.

Crossrefs

Cf. A001742 (version 2).

Programs

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 *)

Formula

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

Extensions

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