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%I #26 Nov 29 2019 18:26:53
%S 2,4,8,24,48,288,864,6048,260064,26266464,40082624064,866826828008064,
%T 26444286042042008448,20286626620462624006244884224,
%U 22488068646246262608620204848404846444288,284860000088022466828484860444044822420060828284646488064
%N a(1) = 2, a(n+1) > a(n) is the smallest multiple of a(n) using only even digits but not divisible by 10 (i.e., having no trailing zeros).
%t a[n_] := a[n] = Block[{k = 2, b = a[n - 1], c = 2 Range[0, 4]}, While[Mod[k*b,10]==0 || Union@ Join[c, IntegerDigits[k*b]] != c, k++]; k*b]; a[1] = 2; Array[a,14] (* _Robert G. Wilson v_, May 26 2014 *)
%Y Cf. A078221, A078222, A078224.
%K nonn,base
%O 1,1
%A _Amarnath Murthy_, Nov 23 2002
%E More terms from _Sascha Kurz_, Jan 06 2003
%E a(14) from _Jon E. Schoenfield_, Jun 04 2007
%E a(15) from _Chai Wah Wu_, Nov 20 2019
%E a(16) from _Chai Wah Wu_, Nov 29 2019