A059175 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.
0, 66, 66, 462, 180, 66, 31395, 714, 72, 9, 5, 15, 3, 36, 42, 39, 2, 9, 45, 462, 12, 12, 90, 3703207920, 1692600, 84, 234, 27, 3043425, 74613, 6, 7930296, 264, 4290, 510, 315, 315, 73302369360, 1155, 3, 8, 239872017, 6, 4386, 1989, 18, 17740866, 499954980
Offset: 0
Examples
3/1 -> 3/4 -> 12/7 -> 84/10=42/5 -> 210/11 -> 2310/5 = 462 so a(3)=462. 84/1 -> 84/13 -> 273/4 -> 273/4 -> ... so a(84) = 0.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
- P. Schogt, The Wild Number Problem: math or fiction?, arXiv preprint arXiv:1211.6583 [math.HO], 2012. - From _N. J. A. Sloane_, Jan 03 2013
Programs
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Haskell
import Data.Ratio ((%), numerator, denominator) a059175 n = f [n % 1] where f xs@(x:_) | denominator y == 1 = numerator y | y `elem` xs = 0 | otherwise = f (y : xs) where y = (numerator x * denominator x) % (a007953 (numerator x) + a007953 (denominator x)) -- Reinhard Zumkeller, Mar 11 2013 -
Mathematica
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 *) -
PARI
f2(p,q) = p*q/(sumdigits(p)+sumdigits(q)); f1(r) = f2(numerator(r), denominator(r)); loop(list) = {my(v=Vecrev(list)); for (i=2, #v, if (v[i] == v[1], return(1)););} 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
Formula
a(A214866(n)) = 0. - Reinhard Zumkeller, Mar 11 2013
Extensions
Corrected and extended by Naohiro Nomoto, Jul 20 2001
Comments