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A001729
List of numbers whose digits contain no loops (version 1).
3
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
1,2
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
Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
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
KEYWORD
base,nonn,easy
EXTENSIONS
Missing 42 and 44 added by T. D. Noe, Aug 10 2012
STATUS
approved