A077696 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).

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

Offset

0,1

Comments

"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.

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

Links

Table of n, a(n) for n=0..11.

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:
print1(a=2); for(n=0, 10, print1(", "a=A077696(1, a))) \\ M. F. Hasler, Nov 18 2018

Crossrefs

Cf. A077697.

Sequence in context: A179420 A346186 A080487 * A326361 A117271 A372179

Adjacent sequences: A077693 A077694 A077695 * A077697 A077698 A077699

Keyword

base,nonn

Author

Amarnath Murthy, Nov 18 2002

Extensions

Corrected and extended by Ray Chandler, Jul 25 2003

Definition edited by M. F. Hasler, Nov 18 2018

Status

approved