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A140488 Trajectory of 5 under repeated application of the map: n -> n + second-smallest number that does not divide n.

%I A140488 #16 Oct 19 2021 20:16:56
%S A140488 5,8,13,16,21,25,28,33,37,40,46,50,54,59,62,66,71,74,78,83,86,90,97,
%T A140488 100,106,110,114,119,122,126,131,134,138,143,146,150,157,160,166,170,
%U A140488 174,179,182,186,191,194,198,203,206,210,218,222,227,230,234,239,242,246
%N A140488 Trajectory of 5 under repeated application of the map: n -> n + second-smallest number that does not divide n.
%H A140488 Robert Israel, <a href="/A140488/b140488.txt">Table of n, a(n) for n = 1..10000</a>
%F A140488 It appears that a(n+98) = a(n)+420 for n >= 9. - _Robert Israel_, Oct 19 2021
%p A140488 f:= proc(n) local k,c;
%p A140488 c:= 0:
%p A140488 for k from 2 do
%p A140488   if n mod k <> 0 then
%p A140488     if c = 1 then return n+k fi;
%p A140488     c:= 1;
%p A140488   fi
%p A140488 od
%p A140488 end proc:
%p A140488 R:= 5: t:= 5:
%p A140488 for count from 2 to 100 do
%p A140488   t:= f(t);
%p A140488   R:= R,t;
%p A140488 od:
%p A140488 R; # _Robert Israel_, Oct 19 2021
%t A140488 a = {5}; Do[AppendTo[a, a[[ -1]] + Select[Range[a[[ -1]]], Mod[a[[ -1]], # ] > 0 &][[2]]], {60}]; a (* _Stefan Steinerberger_, Jul 01 2008 *)
%o A140488 (Python)
%o A140488 def aupton(terms):
%o A140488     alst = [5]
%o A140488     while len(alst) < terms:
%o A140488         an, k, smallest = alst[-1], 2, False
%o A140488         while not smallest or an%k == 0:
%o A140488             if not smallest and an%k != 0: smallest = True
%o A140488             k += 1
%o A140488         alst.append(an+k)
%o A140488     return alst
%o A140488 print(aupton(58)) # _Michael S. Branicky_, Oct 19 2021
%Y A140488 Cf. A140485, A140486, A140487, A140489.
%K A140488 nonn
%O A140488 1,1
%A A140488 _Eric Angelini_, Jun 25 2008
%E A140488 Corrected and extended by _Stefan Steinerberger_, Jul 01 2008