cp's OEIS Frontend

A352541 Number of iterations of A352544 (half if even, add largest anagram if odd) until a value is reached for the second time; 0 if this never happens.

%I A352541 #17 Mar 30 2022 06:17:55
%S A352541 1,2,2,2,3,2,2,2,4,2,2,2,3,4,2,3,5,5,2,3,3,2,2,3,4,3,5,3,3,5,4,2,6,2,
%T A352541 6,5,3,3,4,4,4,2,2,2,3,3,4,5,5,21,4,2,6,2,4,2,4,4,6,3,5,2,2,2,7,2,2,
%U A352541 21,7,7,6,2,4,2,4,2,5,2,5,6,5,2,2,2,3,2,2,2,4,0,4
%N A352541 Number of iterations of A352544 (half if even, add largest anagram if odd) until a value is reached for the second time; 0 if this never happens.
%C A352541 A352544 is a variant of the Collatz map, where for an odd argument x, the number A004186(x) (= digits of x arranged in decreasing order) is added.
%C A352541 The first zero appears for initial value n = 89. See A352542 for the trajectory of n = 89. See A352540 for the indices of zeros.
%H A352541 Eric Angelini, <a href="https://mailman.xmission.com/hyperkitty/list/math-fun@mailman.xmission.com/thread/RI5P2MYI7NKD32LK47XTYTGUAEMQKVVZ/">Divide by 2 or add the biggest anagram</a>, math-fun discussion list, Mar 20 2022
%F A352541 a(n) = 0 iff n is in A352540.
%e A352541 The trajectory of n = 4 is 4 -> 8 -> 16 -> 8 -> 16 -> .... The value 8 is the first one to appear for a second time after the third iteration, therefore a(4) = 3.
%e A352541 a(8) = 4 because the trajectory of 8 is 8 -> 4 -> 2 -> 1 -> 2 -> 1 ..., so the number 2 is the first one to appear for a second time, after the 4th iteration of the map A352544.
%e A352541 The trajectory of n = 49 is (49, 143, 574, 287, 1159, 10670, 5335, 10868, 5434, 2717, 10438, 5219, 14740, 7370, 3685, 12338, 6169, 15830, 7915, 17666, 8833, 17666, 8833, ...): The number 17666 is the first one to appear for a second time, after the (a(49) = 21)-st iteration.
%o A352541 (PARI) apply( {A352541(n,U=[n],L=200)=for(i=1,L, setsearch(U,n=A352544(n))&& return(i); U=setunion(U,[n]))}, [0..99])
%Y A352541 Cf. A352544 (half or add largest anagram), A004186 (largest anagram: arrange digits in decreasing order).
%Y A352541 Cf. A352542 (trajectory of 89 under A352544), A352540 (indices of zeros).
%K A352541 nonn,base
%O A352541 0,2
%A A352541 _M. F. Hasler_, Mar 20 2022