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 A057684 Trajectory of 13 under the '13x+1' map. 8
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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 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 *) CROSSREFS Cf. A057446, A057216, A057522, A057534, A057614. See also A033478, A057688, A057684, A057685, A057686, A057687, A057689, A057690, A057691. Sequence in context: A176596 A176023 A067220 * A053153 A167254 A140455 Adjacent sequences:  A057681 A057682 A057683 * A057685 A057686 A057687 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 20 2000 STATUS approved

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Last modified January 18 15:07 EST 2022. Contains 350455 sequences. (Running on oeis4.)