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A057684 Trajectory of 13 under the '13x+1' map.

%I A057684 #19 Dec 06 2023 14:17:55
%S A057684 13,170,85,17,222,111,37,482,241,3134,1567,20372,10186,5093,463,6020,
%T A057684 3010,1505,301,43,560,280,140,70,35,7,1,14,7,1,14,7,1,14,7,1,14,7,1,
%U A057684 14,7,1,14,7,1,14,7,1,14,7,1,14,7,1,14,7,1,14,7,1,14,7
%N A057684 Trajectory of 13 under the '13x+1' map.
%C A057684 The 'Px+1 map': if x is divisible by any prime < P then divide out these primes one at a time starting with the smallest; otherwise multiply x by P and add 1.
%H A057684 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%p A057684 with(numtheory): a := proc(n,S,Q) option remember: local k; if n=0 then RETURN(S); fi: for k from 1 to Q do if a(n-1,S,Q) mod ithprime(k) = 0 then RETURN(a(n-1,S,Q)/ithprime(k)); fi: od: RETURN(ithprime(Q+1)*a(n-1,S,Q)+1) end; # run with S=13 and Q=5.
%t A057684 a[n_, S_, Q_] := a[n, S, Q] = Module[{k}, If[n == 0, S, For[k = 1, k <= Q, k++, If[Mod[a[n-1, S, Q], Prime[k]] == 0, Return[a[n-1, S, Q]/Prime[k]]] ]; Prime[Q+1]*a[n-1, S, Q] + 1]];
%t A057684 Table[a[n, 13, 5], {n, 0, 60}] (* _Jean-François Alcover_, Jul 13 2016, adapted from Maple *)
%Y A057684 Cf. A057446, A057216, A057522, A057534, A057614. See also A033478, A057688, A057685, A057686, A057687, A057689, A057690, A057691.
%K A057684 nonn,easy
%O A057684 0,1
%A A057684 _N. J. A. Sloane_, Oct 20 2000