

A257275


Numbers equal to some partial product of the sequence of their digits, repeated over and over again.


1



1, 2, 3, 4, 5, 6, 7, 8, 9, 735, 18432, 442368, 3682784876146817236992
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The sequence is conjectured to be finite (D. Wilson, Reply on the SeqFan list).
There are no additional terms below 10^300.  Max Alekseyev, Apr 29 2015


LINKS

Table of n, a(n) for n=1..13.
E. Angelini (and replies by H. P. Dale and D. Wilson), Cumulative multiplication, April 18, 2015
C. Meller, 1392  Producto acumulado, April 21, 2015.
C. Rivera, Puzzle 784: Find some more solutions, April 25, 2015


EXAMPLE

735 = 7 * 3 * 5 * 7
18432 = 1 * 8 * 4 * 3 * 2 * 1 * 8 * 4 * 3
442368 = 4 * 4 * 2 * 3 * 6 * 8 * 4 * 4 * 2 * 3
3682784876146817236992 = A007954(3682784876146817236992) * A007954(3682784876).  Giovanni Resta, Apr 29 2015.


MATHEMATICA

Select[Range[450000], MemberQ[FoldList[Times, PadRight[{}, 50, IntegerDigits[#]]], #]&] (* The program will generate the first 12 terms of the sequence. *) (* Harvey P. Dale, Jun 21 2017 *)


PROG

(PARI) is(n, d=digits(n), p=1)=for(i=0, n, (n>p*=d[i%#d+1])return(n==p))


CROSSREFS

Subsequence of A007602 and likely of A128606 and A257554.  Max Alekseyev, Apr 29 2015
Sequence in context: A069747 A308126 A124107 * A112014 A145461 A075154
Adjacent sequences: A257272 A257273 A257274 * A257276 A257277 A257278


KEYWORD

nonn,base,more


AUTHOR

M. F. Hasler, Apr 29 2015


EXTENSIONS

a(12) from Harvey P. Dale, Apr 18 2015
a(13) from Giovanni Resta, Apr 29 2015


STATUS

approved



