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

13, 170, 85, 17, 222, 111, 37, 482, 241, 3134, 1567, 20372, 10186, 5093, 463, 6020, 3010, 1505, 301, 43, 560, 280, 140, 70, 35, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7, 1, 14, 7

Offset: 0

Author

N. J. A. Sloane, Oct 20 2000

Keywords

• nonn
• easy

Comments

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.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,1).

Crossrefs

Cf. A057446, A057216, A057522, A057534, A057614. See also A033478, A057688, A057685, A057686, A057687, A057689, A057690, A057691.

Programs

Maple

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.

Mathematica

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]];
Table[a[n, 13, 5], {n, 0, 60}] (* Jean-François Alcover, Jul 13 2016, adapted from Maple *)