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A256240
Numbers n such that repeatedly setting n := A066308(n) yields a constant nonzero n.
2
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
Sequence in context: A260807 A178917 A159026 * A090062 A166370 A240510
KEYWORD
nonn,base
AUTHOR
David A. Corneth, Mar 20 2015
STATUS
approved