A117121 Numbers k for which none of the digits of k appear in the decimal expansion of 1/k.

2, 4, 5, 8, 9, 11, 12, 15, 18, 22, 25, 36, 39, 44, 45, 55, 66, 72, 74, 75, 88, 99, 111, 125, 132, 135, 148, 182, 198, 222, 225, 239, 259, 264, 271, 275, 296, 351, 369, 375, 378, 396, 399, 444, 455, 478, 481, 495, 525, 555, 585, 666, 675, 876, 888, 925, 984

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..192

Example

39 is in the sequence because in the decimal expansion of 1/39 = 0.02564102564102564... there are no 3's and 9's.
167 is not in the sequence because the decimal expansion of 1/167 = 0.005988023952095808383233532934131736... includes 1, 6 and 7.

Mathematica

q[n_] := Module[{r = RealDigits[1/n], d = IntegerDigits[n]}, If[r[[2]] < 0, ! MemberQ[d, 0], True] && !IntersectingQ[d, Flatten@r[[1]]]]; Select[Range[1000], q] (* Amiram Eldar, Mar 24 2021 *)

Crossrefs

Subsequence of A052382.

A002275 \ {0, 1} is a subsequence.

Sequence in context: A201818 A047380 A288214 * A101925 A101884 A118179

Adjacent sequences: A117118 A117119 A117120 * A117122 A117123 A117124

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 19 2006

Extensions

Corrected by T. D. Noe, Nov 01 2006

Offset corrected and a wrong term (167) removed by Amiram Eldar, Mar 24 2021

Status

approved