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A061811 Multiples of 3 with all even digits.

%I A061811 #12 May 03 2025 16:16:00
%S A061811 0,6,24,42,48,60,66,84,204,222,228,240,246,264,282,288,402,408,420,
%T A061811 426,444,462,468,480,486,600,606,624,642,648,660,666,684,804,822,828,
%U A061811 840,846,864,882,888,2004,2022,2028,2040,2046,2064,2082,2088,2202,2208
%N A061811 Multiples of 3 with all even digits.
%C A061811 The numbers b(d) of terms from 10^(d-1) to 10^d satisfy the recurrence b(d) = 6 b(d-1) - 6 b(d-2) + 5 b(d-3) with b(1)=1, b(2)=6, b(3)=33.  For d >= 4, b(d) = (3*A276508(d) - 10*A276508(d-1) + 3*A276508(d-2))/7. - _Robert Israel_, Feb 15 2017
%H A061811 Robert Israel, <a href="/A061811/b061811.txt">Table of n, a(n) for n = 1..10000</a>
%H A061811 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%e A061811 228 has all even digits and 228 = 3*76.
%p A061811 N:= 4: # for all terms < 10^N
%p A061811 E[1,0]:= {6}:
%p A061811 E[1,1]:= {4}:
%p A061811 E[1,2]:= {2,8}:
%p A061811 for n from 2 to N do
%p A061811   for j from 0 to 2 do
%p A061811     E[n,j]:= map(t -> (10*t, 10*t+6),E[n-1,j]) union
%p A061811              map(t -> (10*t+2, 10*t+8), E[n-1,j+1 mod 3]) union
%p A061811            map(t -> 10*t+4, E[n-1,j+2 mod 3]);
%p A061811 od od:
%p A061811 A:=sort([0,seq(op(E[i,0]),i=1..N)]); # _Robert Israel_, Feb 15 2017
%t A061811 Select[3*Range[0,800],AllTrue[IntegerDigits[#],EvenQ]&] (* _Harvey P. Dale_, May 03 2025 *)
%o A061811 (PARI) is(n)=n%3==0 && #setintersect(Set(digits(n)), [1,3,5,7,9])==0 \\ _Charles R Greathouse IV_, Feb 15 2017
%Y A061811 Cf. A061810, A276508.
%K A061811 nonn,base,easy
%O A061811 1,2
%A A061811 _Amarnath Murthy_, May 28 2001
%E A061811 More terms from Larry Reeves (larryr(AT)acm.org), May 30 2001
%E A061811 Offset corrected by _Charles R Greathouse IV_, Feb 15 2017