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

Author

M. F. Hasler, Apr 29 2015

Keywords

• nonn
• base
• more

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

Examples

			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.
		

Links

• 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

Crossrefs

Subsequence of A007602 and likely of A128606 and A257554. - Max Alekseyev, Apr 29 2015

Programs

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 *)

PARI

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

Extensions

a(12) from Harvey P. Dale, Apr 18 2015

a(13) from Giovanni Resta, Apr 29 2015