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

Author

Reinhard Zumkeller, Mar 26 2008

Keywords

• nonn
• base
• easy

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.

Crossrefs

Cf. A007090, A091633 (primes), A245193.

Programs

Haskell

import Data.List (intersect)
a136333 n = a136333_list !! (n-1)
a136333_list = filter (null . intersect "024568" . show) [1..]
-- Reinhard Zumkeller, Jul 17 2014

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 *)

PARI

isok(m) = my(d=digits(m)); apply(x->gcd(x, 10), d) == vector(#d, k, 1); \\ Michel Marcus, Feb 25 2022

Formula

Sum_{n>=1} 1/a(n) = 2.395867871130444522329053889312125689319669370758630349552737883715872077555... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 15 2024