cp's OEIS Frontend

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

%I A256240 #26 Feb 16 2025 08:33:25
%S A256240 1,89,98,135,139,144,153,193,233,315,319,323,332,351,391,414,441,513,
%T A256240 531,913,931,1224,1242,1367,1376,1422,1637,1673,1736,1763,2124,2142,
%U A256240 2214,2241,2412,2421,3167,3176,3617,3671,3716,3761,4122,4212
%N A256240 Numbers n such that repeatedly setting n := A066308(n) yields a constant nonzero n.
%C A256240 Eventually, these values of n become nonzero elements of A038369; 1, 135 or 144.
%H A256240 Chai Wah Wu, <a href="/A256240/b256240.txt">Table of n, a(n) for n = 1..10000</a> (terms n = 1..869 from David A. Corneth).
%H A256240 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sum-ProductNumber.html">Sum-Product Number</a>
%e A256240 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.
%t A256240 Select[Range[5000], FixedPoint[Total[#] Apply[Times, #] &@ IntegerDigits@ # &, #] > 0 &] (* _Michael De Vlieger_, Aug 16 2017 *)
%o A256240 (PARI) \\test if n is an element.
%o A256240 is(n)=while(n!=SP(n),n=SP(n));n>0
%o A256240 \\Sum of digits times product of digits of n (A066308(n))
%o A256240 SP(n)={d=digits(n);prod(i=1,#d,d[i])*vecsum(d)}
%Y A256240 Cf. A038369, A066308.
%K A256240 nonn,base
%O A256240 1,2
%A A256240 _David A. Corneth_, Mar 20 2015