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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. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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, 2012. - From N. J. A. Sloane, Jan 03 2013

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

Cf. A058971, A058972.

Cf. A008472, A001221.

Cf. A247462, A247468.

Sequence in context: A192141 A092556 A092550 * A085818 A270709 A323382

Adjacent sequences:  A058974 A058975 A058976 * A058978 A058979 A058980

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Jan 14 2001

EXTENSIONS

More terms from Matthew Conroy, Apr 18 2001

STATUS

approved

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Last modified July 17 21:36 EDT 2019. Contains 325109 sequences. (Running on oeis4.)