A136333 Numbers containing only digits coprime to 10 in their decimal representation.

1, 3, 7, 9, 11, 13, 17, 19, 31, 33, 37, 39, 71, 73, 77, 79, 91, 93, 97, 99, 111, 113, 117, 119, 131, 133, 137, 139, 171, 173, 177, 179, 191, 193, 197, 199, 311, 313, 317, 319, 331, 333, 337, 339, 371, 373, 377, 379, 391, 393, 397, 399, 711, 713, 717, 719, 731

Offset

1,2

Comments

Numbers containing digits 1,3,7,9 only, or, numbers written in base 4 (cf. A007090) with digits mapped by: 0->1, 1->3, 2->7 and 3->9. - Reinhard Zumkeller, Jul 17 2014

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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) = 2.395867871130444522329053889312125689319669370758630349552737883715872077555... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 15 2024

Mathematica

fQ[n_] := Block[{s = {1, 3, 7, 9}}, Union[Join[s, IntegerDigits@ n]] == s]; Select[ Range@ 1000, fQ] (* or *)
depth = 3; FromDigits@# & /@ FlattenAt[ Table[ Tuples[{1, 3, 7, 9}, n], {n, depth}], {#} & /@ Range[depth]] (* Robert G. Wilson v, Jul 02 2014 *)

Prog

(Haskell)
import Data.List (intersect)
a136333 n = a136333_list !! (n-1)
a136333_list = filter (null . intersect "024568" . show) [1..]
-- Reinhard Zumkeller, Jul 17 2014
(PARI) isok(m) = my(d=digits(m)); apply(x->gcd(x, 10), d) == vector(#d, k, 1); \\ Michel Marcus, Feb 25 2022

Crossrefs

Cf. A007090, A091633 (primes), A245193.

Sequence in context: A080903 A172253 A104381 * A134454 A324695 A113522

Adjacent sequences: A136330 A136331 A136332 * A136334 A136335 A136336

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Mar 26 2008

Status

approved