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

Author

David A. Corneth, Mar 20 2015

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

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

Crossrefs

Cf. A038369, A066308.

Programs

Mathematica

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

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)}