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
KEYWORD
nonn,base
AUTHOR
David A. Corneth, Mar 20 2015
STATUS
approved