A256240 Numbers n such that repeatedly setting n := A066308(n) yields a constant nonzero n.

1, 89, 98, 135, 139, 144, 153, 193, 233, 315, 319, 323, 332, 351, 391, 414, 441, 513, 531, 913, 931, 1224, 1242, 1367, 1376, 1422, 1637, 1673, 1736, 1763, 2124, 2142, 2214, 2241, 2412, 2421, 3167, 3176, 3617, 3671, 3716, 3761, 4122, 4212

Offset

1,2

Comments

Eventually, these values of n become nonzero elements of A038369; 1, 135 or 144.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..869 from David A. Corneth).

Eric Weisstein's World of Mathematics, Sum-Product Number

Example

89 is an element because (8 + 9) * 8 * 9 = 1224, then (1 + 2 + 2 + 4) * 1 * 2 * 2 * 4 = 144, then (1 + 4 + 4) * 1 * 4 * 4 = 144. Repetition so stop. 144 > 0 so 89 is an element.

Mathematica

Select[Range[5000], FixedPoint[Total[#] Apply[Times, #] &@ IntegerDigits@ # &, #] > 0 &] (* Michael De Vlieger, Aug 16 2017 *)

Prog

(PARI) \\test if n is an element.
is(n)=while(n!=SP(n), n=SP(n)); n>0
\\Sum of digits times product of digits of n (A066308(n))
SP(n)={d=digits(n); prod(i=1, #d, d[i])*vecsum(d)}

Crossrefs

Cf. A038369, A066308.

Sequence in context: A260807 A178917 A159026 * A090062 A166370 A240510

Adjacent sequences: A256237 A256238 A256239 * A256241 A256242 A256243

Keyword

nonn,base

Author

David A. Corneth, Mar 20 2015

Status

approved