

A257299


Numbers n for which each of the digits 09 appears exactly once as first digit in the orbit of n under iterations of n > (first digit of n)*(n with first digit removed) until a single digit is reached; no leading zeros allowed.


2



9848, 51948, 56648, 68648, 77712, 84157, 87207, 98142, 98642, 249217, 298242, 325803, 328957, 381082, 383003, 423027, 461992, 516957, 549492, 721712, 796523, 812157, 879707, 925492, 945992, 948742, 950742, 960492, 1248242, 1957313, 2211992, 2259492, 2282707
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OFFSET

1,1


COMMENTS

Numbers for which a leading zero appears in "n with first digit removed" are excluded from this sequence. One could consider the variant where this is allowed in case of a "multi digit zero", i.e., if the last step is x0...0 > x*0...0 > 0, see the example of 79855.
The sequence is necessarily finite, because the considered iterations must end in 0 and reach one of the 9 values {10, 20, ..., 90} just before this last iteration, and there must be exactly 9 iterations. This leaves only a finite number of possible starting values n.


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..55 (a(1)a(54) from M. F. Hasler)
L. Blomberg, in reply to E. Angelini, 10line tables ?, SeqFan list, Apr 28 2015


EXAMPLE

a(1) = 9848 is in the sequence because if we consider 9848 > 9 * 848 = 7632 > 7 * 632 = 4424 > 4 * 424 = 1696 > 1 * 696 = 696 > 6 * 96 = 576 > 5 * 76 = 380 > 3 * 80 = 240 > 2 * 40 = 80 > 8 * 0 = 0, each of the digits 09 appears exactly once as first digit.
For a(2) = 51948, the sequence is 51948 > 9740 > 6660 > 3960 > 2880 > 1760 > 760 > 420 > 80 > 0.
For 79855 > 68985 > 53910 > 19550 > 9550 > 4950 > 3800 > 2400 > 800 > 0, there appears a "leading zero", but only in front of zero.
a(54) = 24578492 is in the sequence because it yields the sequence 24578492 > 9156984 > 1412856 > 412856 > 51424 > 7120 > 840 > 320 > 60 > 0.


PROG

(PARI) is(n, d=0)={while(n, bittest(d, (n=divrem(n, 10^L=#Str(n\10)))[1])&&return; #Str(n[2])==Lreturn; d+=1<<n[1]; n=n[1]*n[2]); d==2^102}
(Python)
from itertools import permutations
A257299_list = []
for n in permutations('123456789', 9):
....x = 0
....for d in n:
........q, r = divmod(x, int(d))
........if r:
............break
........x = int(d + str(q))
....else:
........A257299_list.append(x)
A257299_list = sorted(A257299_list) # Chai Wah Wu, May 11 2015
(PARI) A257299(v=0, d=vector(9, i, i))={Set(concat(vector(#d, i, if(v%d[i], [], if(#d>1, A257299(eval(Str(d[i], v/d[i])), vecextract(d, Str("^"i))), [eval(Str(d[i], v/d[i]))])))))} \\ Use just A257299() for the complete list.  M. F. Hasler, May 11 2015


CROSSREFS

Sequence in context: A196897 A022199 A203809 * A208646 A001230 A238076
Adjacent sequences: A257296 A257297 A257298 * A257300 A257301 A257302


KEYWORD

nonn,base,fini,full


AUTHOR

Eric Angelini and M. F. Hasler, May 08 2015


STATUS

approved



