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Numbers that contain only the digits 0,4,8. Permutable multiples of 4: numbers k such that every permutation of the digits of k is a multiple of 4.
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%I #15 May 07 2021 01:06:55

%S 0,4,8,40,44,48,80,84,88,400,404,408,440,444,448,480,484,488,800,804,

%T 808,840,844,848,880,884,888,4000,4004,4008,4040,4044,4048,4080,4084,

%U 4088,4400,4404,4408,4440,4444,4448,4480,4484,4488,4800,4804

%N Numbers that contain only the digits 0,4,8. Permutable multiples of 4: numbers k such that every permutation of the digits of k is a multiple of 4.

%C Also permutable multiples of 4: numbers k such that every permutation of the digits of k is a multiple of 4.

%F a(n) = 4*A007089(n).

%e 480 = 4*120, 408 = 4*102, 840 = 4*210, 804 = 4*201, 048 = 4*12, 084 = 4*21.

%p f:= proc(n) local L,i;

%p L:= convert(n,base,3);

%p 4*add(L[i]*10^(i-1),i=1..nops(L))

%p end proc:

%p map(f, [$0..100]); # _Robert Israel_, Apr 30 2021

%t FromDigits /@ Tuples[{0, 4, 8}, 4] (* _Amiram Eldar_, Apr 30 2021 *)

%o (PARI) a(n) = fromdigits(digits(n, 3))*4 \\ _Rémy Sigrist_, May 05 2021

%Y Cf. A003459, A007089, A008585, A008586, A014263, A061811, A169964.

%K nonn,base,easy

%O 0,2

%A _Ctibor O. Zizka_, Apr 30 2021