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A257275 Numbers equal to some partial product of the sequence of their digits, repeated over and over again. 1

%I

%S 1,2,3,4,5,6,7,8,9,735,18432,442368,3682784876146817236992

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

%C The sequence is conjectured to be finite (D. Wilson, Reply on the SeqFan list).

%C There are no additional terms below 10^300. - _Max Alekseyev_, Apr 29 2015

%H E. Angelini (and replies by H. P. Dale and D. Wilson), <a href="http://list.seqfan.eu/pipermail/seqfan/2015-April/014744.html">Cumulative multiplication</a>, April 18, 2015

%H C. Meller, <a href="http://simplementenumeros.blogspot.mx/2015/04/1392-producto-acumulado.html#comment-form">1392 - Producto acumulado</a>, April 21, 2015.

%H C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_784.htm">Puzzle 784: Find some more solutions</a>, April 25, 2015

%e 735 = 7 * 3 * 5 * 7

%e 18432 = 1 * 8 * 4 * 3 * 2 * 1 * 8 * 4 * 3

%e 442368 = 4 * 4 * 2 * 3 * 6 * 8 * 4 * 4 * 2 * 3

%e 3682784876146817236992 = A007954(3682784876146817236992) * A007954(3682784876). - _Giovanni Resta_, Apr 29 2015.

%t 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 *)

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

%Y Subsequence of A007602 and likely of A128606 and A257554. - _Max Alekseyev_, Apr 29 2015

%K nonn,base,more

%O 1,2

%A _M. F. Hasler_, Apr 29 2015

%E a(12) from _Harvey P. Dale_, Apr 18 2015

%E a(13) from _Giovanni Resta_, Apr 29 2015

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Last modified July 9 16:50 EDT 2020. Contains 335545 sequences. (Running on oeis4.)