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%I #26 Feb 15 2024 01:56:01
%S 1,3,7,9,11,13,17,19,31,33,37,39,71,73,77,79,91,93,97,99,111,113,117,
%T 119,131,133,137,139,171,173,177,179,191,193,197,199,311,313,317,319,
%U 331,333,337,339,371,373,377,379,391,393,397,399,711,713,717,719,731
%N Numbers containing only digits coprime to 10 in their decimal representation.
%C 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
%H Reinhard Zumkeller, <a href="/A136333/b136333.txt">Table of n, a(n) for n = 1..10000</a>
%H Robert Baillie and Thomas Schmelzer, <a href="https://library.wolfram.com/infocenter/MathSource/7166/">Summing Kempner's Curious (Slowly-Convergent) Series</a>, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F Sum_{n>=1} 1/a(n) = 2.395867871130444522329053889312125689319669370758630349552737883715872077555... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 15 2024
%t fQ[n_] := Block[{s = {1, 3, 7, 9}}, Union[Join[s, IntegerDigits@ n]] == s]; Select[ Range@ 1000, fQ] (* or *)
%t depth = 3; FromDigits@# & /@ FlattenAt[ Table[ Tuples[{1, 3, 7, 9}, n], {n, depth}], {#} & /@ Range[depth]] (* _Robert G. Wilson v_, Jul 02 2014 *)
%o (Haskell)
%o import Data.List (intersect)
%o a136333 n = a136333_list !! (n-1)
%o a136333_list = filter (null . intersect "024568" . show) [1..]
%o -- _Reinhard Zumkeller_, Jul 17 2014
%o (PARI) isok(m) = my(d=digits(m)); apply(x->gcd(x, 10), d) == vector(#d, k, 1); \\ _Michel Marcus_, Feb 25 2022
%Y Cf. A007090, A091633 (primes), A245193.
%K nonn,base,easy
%O 1,2
%A _Reinhard Zumkeller_, Mar 26 2008
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