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%I #21 Feb 09 2022 09:04:41
%S 0,66,66,462,180,66,31395,714,72,9,5,15,3,36,42,39,2,9,45,462,12,12,
%T 90,3703207920,1692600,84,234,27,3043425,74613,6,7930296,264,4290,510,
%U 315,315,73302369360,1155,3,8,239872017,6,4386,1989,18,17740866,499954980
%N For a rational number p/q let f(p/q) = p*q divided by the sum of digits of p and q; a(n) is obtained by iterating f, starting at n/1, until an integer is reached, or if no integer is ever reached then a(n) = 0.
%H Reinhard Zumkeller, <a href="/A059175/b059175.txt">Table of n, a(n) for n = 0..10000</a>
%H P. Schogt, <a href="http://arxiv.org/abs/1211.6583">The Wild Number Problem: math or fiction?</a>, arXiv preprint arXiv:1211.6583 [math.HO], 2012. - From _N. J. A. Sloane_, Jan 03 2013
%F a(A214866(n)) = 0. - _Reinhard Zumkeller_, Mar 11 2013
%e 3/1 -> 3/4 -> 12/7 -> 84/10=42/5 -> 210/11 -> 2310/5 = 462 so a(3)=462.
%e 84/1 -> 84/13 -> 273/4 -> 273/4 -> ... so a(84) = 0.
%t f[Rational[p_, q_]] := p*q/(Total[ IntegerDigits[p]] + Total[ IntegerDigits[q]]); f[n_Integer] := n/(1 + Total[ IntegerDigits[n]]); a[n_] := If[ IntegerQ[ r = NestWhile[f, n, Not[#1 == #2 || #1 != #2 && IntegerQ[#2]]&, 2]], r, 0]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Apr 03 2013 *)
%o (Haskell)
%o import Data.Ratio ((%), numerator, denominator)
%o a059175 n = f [n % 1] where
%o f xs@(x:_) | denominator y == 1 = numerator y
%o | y `elem` xs = 0
%o | otherwise = f (y : xs)
%o where y = (numerator x * denominator x) %
%o (a007953 (numerator x) + a007953 (denominator x))
%o -- _Reinhard Zumkeller_, Mar 11 2013
%o (PARI) f2(p,q) = p*q/(sumdigits(p)+sumdigits(q));
%o f1(r) = f2(numerator(r), denominator(r));
%o loop(list) = {my(v=Vecrev(list)); for (i=2, #v, if (v[i] == v[1], return(1)););}
%o a(n) = {if (n==0, return(0)); my(ok=0, m=f2(n,1), list=List()); while(denominator(m) != 1, m = f1(m); listput(list, m); if (loop(list), return (0));); return(m);} \\ _Michel Marcus_, Feb 09 2022
%Y Cf. A007953, A058971, A214866.
%K base,easy,nonn,nice
%O 0,2
%A _Floor van Lamoen_, Jan 15 2001
%E Corrected and extended by _Naohiro Nomoto_, Jul 20 2001
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