A247462 -id:A247462 - cp's OEIS frontend

A247468 Smallest number m such that A247462(m) = n.

1, 5, 164, 501, 7364, 29121, 515504, 2445693, 92781321

Offset: 1

Reinhard Zumkeller, Sep 17 2014

			.  n |    a(n) |                  A058977 trajectory
. ---+---------+---------------------------------------------------------
.  2 |       5 | 1/a(2)-5/2-7
.  3 |     164 | 1/a(3)-19/3-13/2-4
.  4 |     501 | 1/a(4)-253/2-25/3-9/2-11
.  5 |    7364 | 1/a(5)-499/3-253/2-25/3-9/2-11
.  6 |   29121 | 1/a(6)-14563/2-979/3-493/2-19/3-13/2-4
.  7 |  515504 | 1/a(6)-34375/3-17191/2-535/3-271/2-23/3-15/2-17
.  8 | 2445693 | 1/a(8)-1222849/2-58241/3-14563/2-979/3-493/2-19/3-13/2-4

Cf. A247462, A058977.

import Data.List (elemIndex); import Data.Maybe (fromJust)
a247468 = (+ 1) . fromJust . (`elemIndex` a247462_list)

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)); ); }
f(n) = {my(ok=0, m=f2(n, 1), list=List(), nb=1); while(denominator(m) != 1, m = f1(m); nb++; listput(list, m); if (loop(list), return (0)); ); return(nb); } \\ A247462
a(n) = my(k=1); while(f(k) != n, k++); k; \\ Michel Marcus, Feb 09 2022

A247462(a(n)) = n and A247462(m) < n for m < a(n).

a(9) from Michel Marcus, Feb 09 2022

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.

Original entry on oeis.org

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

N. J. A. Sloane, Jan 14 2001

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

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

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

Cf. A058971, A058972.
Cf. A008472, A001221.
Cf. A247462, A247468.

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

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 *)

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

More terms from Matthew Conroy, Apr 18 2001

cp's OEIS Frontend

A247468 Smallest number m such that A247462(m) = n.

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