A257554 -id:A257554 - cp's OEIS frontend

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

M. F. Hasler, Apr 29 2015

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

			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.

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

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

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 *)

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

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

a(13) from Giovanni Resta, Apr 29 2015

A270393 Another variant of narcissistic numbers: integers n equal the product of squared digits of n divided by the sum of digits of n, i.e., n = A007954(n)^2/A007953(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 36, 735

Offset: 1

José de Jesús Camacho Medina, Mar 16 2016

No other terms below 10^300. - Max Alekseyev, May 31 2018

			36 is a term because 36 = (3^2*6^2)/(3+6).
735 is a term because 735 = (7^2*3^2*5^2)/(7+3+5).

Subsequence of A128606.

Cf. A005188, A257554.

Select[Range[10^6], Function[k, k == Apply[Times, #^2]/(Total@ #) &@ IntegerDigits@ k]@ # &] (* Michael De Vlieger, Mar 16 2016 *)

{ is_A270393(n) = my(d = digits(n)); n == vecprod(d)^2/vecsum(d); } \\ Michel Marcus, Mar 17 2016

cp's OEIS Frontend

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

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