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

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

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