

A077696


a(0) = 2; a(n) = smallest multiple of a(n1), not a multiple of 10, that contains all the digits of a(n1).


6



2, 12, 132, 10032, 7213008, 1017034128, 1374013106928, 1826063419107312, 10056131249023967184, 26980600141131303954672, 287019624301354811469800736, 130880948681417794030229135616
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OFFSET

0,1


COMMENTS

"Contains all the digits of a(n1)" means it can be obtained by inserting digits anywhere in a permutation of digits of a(n1) (prefix, suffix or insertion), but zeros are not to be suffixed as to avoid the trivial solution a(n1)*10.
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(n1)*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


LINKS



PROG

(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:


CROSSREFS



KEYWORD

base,nonn


AUTHOR



EXTENSIONS



STATUS

approved



