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%I #21 Jan 17 2020 10:41:30
%S 2,12,132,10032,7213008,1017034128,1374013106928,1826063419107312,
%T 10056131249023967184,26980600141131303954672,
%U 287019624301354811469800736,130880948681417794030229135616
%N a(0) = 2; a(n) = smallest multiple of a(n-1), not a multiple of 10, that contains all the digits of a(n-1).
%C "Contains all the digits of a(n-1)" means it can be obtained by inserting digits anywhere in a permutation of digits of a(n-1) (prefix, suffix or insertion), but zeros are not to be suffixed as to avoid the trivial solution a(n-1)*10.
%C The 5th term suggested by the original author was 1103520 = 110 * 10032. This lets us guess that the intended definition was to exclude the trivial solution a(n-1)*10, but not any multiple of 10. But the definition has been amended to exclude multiples of 10 completely, and a(5) has been changed to the current value. Similarly, after a(8) = 1826063419107312, there would be a nontrivial solution a(9) = a(8)*5 = 2401273396126115280, where the final 0 is not appended but one of the 0's already in a(8). This is however excluded by the definition. - _M. F. Hasler_, Nov 18 2018
%o (PARI) A077696(n,a=2)={my(c(n,c=vector(10))=for(i=1,#n=digits(n),c[n[i]+1]++);c); for(i=1,n,my(cc=c(a));for(k=2,oo, k%5 && vecmin(c(k*a)-cc)>=0 && (a*=k) && break));a} \\ n=1 and optional 2nd arg as starting value yields next term:
%o print1(a=2);for(n=0,10,print1(","a=A077696(1,a))) \\ _M. F. Hasler_, Nov 18 2018
%Y Cf. A077697.
%K base,nonn
%O 0,1
%A _Amarnath Murthy_, Nov 18 2002
%E Corrected and extended by _Ray Chandler_, Jul 25 2003
%E Definition edited by _M. F. Hasler_, Nov 18 2018