A058977 For a rational number p/q let f(p/q) = sum of distinct prime factors (A008472) of p+q divided by number of distinct prime factors (A001221) of p+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.

2, 3, 2, 5, 7, 7, 2, 3, 3, 11, 7, 13, 11, 4, 2, 17, 7, 19, 3, 5, 4, 23, 7, 5, 17, 3, 11, 29, 13, 31, 2, 7, 5, 6, 7, 37, 23, 8, 3, 41, 4, 43, 4, 4, 3, 47, 7, 7, 3, 10, 17, 53, 7, 8, 11, 11, 7, 59, 13, 61, 6, 5, 2, 9, 19, 67, 5, 13, 17, 71, 7, 73, 41, 4, 23, 9, 6, 79, 3, 3, 4, 83, 4, 11, 47

Offset: 1

Author

N. J. A. Sloane, Jan 14 2001

Keywords

• nonn
• easy
• nice

Comments

A247462 gives number of iterations needed to reach a(n). - Reinhard Zumkeller, Sep 17 2014

Examples

			f(5/1) = 5/2 and f(5/2) = 7, so a(5)=7.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..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

Crossrefs

Cf. A058971, A058972.

Cf. A008472, A001221.

Cf. A247462, A247468.

Programs

Haskell

import Data.Ratio ((%), numerator, denominator)
a058977 = numerator . until ((== 1) . denominator) f . f . fromIntegral
   where f x = a008472 z % a001221 z
               where z = numerator x + denominator x
-- Reinhard Zumkeller, Aug 29 2014

Mathematica

nxt[n_]:=Module[{s=Numerator[n]+Denominator[n]},Total[Transpose[ FactorInteger[ s]][[1]]]/PrimeNu[s]]; Table[NestWhile[nxt,nxt[n],!IntegerQ[#]&],{n,90}] (* Harvey P. Dale, Mar 15 2013 *)

PARI

f2(p,q) = my(f=factor(p+q)[,1]~); vecsum(f)/#f;
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) = {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

Extensions

More terms from Matthew Conroy, Apr 18 2001