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%I #46 May 19 2023 07:01:17
%S 0,45,75,423,445,450,513,750,891,1089,1305,2382,2497,4230,4445,4450,
%T 4488,4491,4500,4505,4513,4878,5013,5045,5130,5133,5868,7317,7500,
%U 7686,8360,8703,8891,8901,8910,8911,8955,8991,9756,9891,10089,10449,10889,10890,10891
%N Numbers k such that 3*k and 7*k share the same set of digits.
%C The sequence is infinite because if k is a term, then 10*k is also a term.
%C Every number k of the form 44...45 (one of more 4's followed by 5, cf. A093140) is a term because 3*k = 133...35 and 7*k = 311...15.
%H Michael S. Branicky, <a href="/A362792/b362792.txt">Table of n, a(n) for n = 1..10000</a>
%e k = 75 is a term because 3*k = 225 and 7*k = 525 share the same set of digits, namely {2,5}.
%e k = 423 is a term because 3*k = 1269 and 7*k = 2961 share the same set of digits, namely {1,2,6,9}.
%t Select[Range[0, 11000], Union[IntegerDigits[3*#]] == Union[IntegerDigits[7*#]] &] (* _Amiram Eldar_, May 18 2023 *)
%o (PARI) isok(k) = Set(digits(3*k)) == Set(digits(7*k));
%o (Python)
%o def ok(n): return set(str(3*n)) == set(str(7*n))
%o print([k for k in range(11000) if ok(k)]) # _Michael S. Branicky_, May 04 2023
%Y Cf. A008585, A008589, A093140.
%K nonn,base,easy
%O 1,2
%A _Alexandru Petrescu_, May 04 2023
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