cp's OEIS Frontend

A057614 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.

%I A057614 #20 Jun 30 2025 17:02:23
%S A057614 17,188,94,47,518,259,37,408,204,102,51,17,188,94,47,518,259,37,408,
%T A057614 204,102,51,17,188,94,47,518,259,37,408,204,102,51,17,188,94,47,518,
%U A057614 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 A057614 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 A057614 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 A057614 Sequence has period 11. - _Alois P. Heinz_, Jan 19 2021
%H A057614 Harvey P. Dale, <a href="/A057614/b057614.txt">Table of n, a(n) for n = 0..1000</a>
%H A057614 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CollatzProblem.html">Collatz problem</a>
%H A057614 <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).
%t A057614 NestList[Which[Mod[#,2]==0,#/2,Mod[#,3]==0,#/3,Mod[#,5]==0,#/5,Mod[#,7]==0,#/7,True,11#+1]&,17,70] (* or *) PadRight[{},100,{17,188,94,47,518,259,37,408,204,102,51}] (* _Harvey P. Dale_, Jun 30 2025 *)
%Y A057614 Cf. A057446, A057216, A057522, A057534.
%K A057614 nonn,easy
%O A057614 0,1
%A A057614 Murad A. AlDamen (Divisibility(AT)yahoo.com), Oct 17 2000