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a(n+1) = a(n)/2 if 2|a(n), a(n)/3 if 3|a(n), a(n)/5 if 5|a(n), a(n)/7 if 7|a(n), otherwise 11*a(n)+1.
14

%I #12 Oct 13 2022 13:01:51

%S 17,188,94,47,518,259,37,408,204,102,51,17,188,94,47,518,259,37,408,

%T 204,102,51,17,188,94,47,518,259,37,408,204,102,51,17,188,94,47,518,

%U 259,37,408,204,102,51,17,188,94,47,518,259,37,408,204,102,51,17,188,94,47,518,259,37,408,204,102,51

%N a(n+1) = a(n)/2 if 2|a(n), a(n)/3 if 3|a(n), a(n)/5 if 5|a(n), a(n)/7 if 7|a(n), otherwise 11*a(n)+1.

%C This is the '11x+1' map. 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.

%C Sequence has period 11. - _Alois P. Heinz_, Jan 19 2021

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CollatzProblem.html">Collatz problem</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,1).

%Y Cf. A057446, A057216, A057522, A057534.

%K nonn,easy

%O 0,1

%A Murad A. AlDamen (Divisibility(AT)yahoo.com), Oct 17 2000