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A352541
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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.
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5
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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, 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, 21, 7, 7, 6, 2, 4, 2, 4, 2, 5, 2, 5, 6, 5, 2, 2, 2, 3, 2, 2, 2, 4, 0, 4
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OFFSET
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0,2
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COMMENTS
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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.
The first zero appears for initial value n = 89. See A352542 for the trajectory of n = 89. See A352540 for the indices of zeros.
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LINKS
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FORMULA
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EXAMPLE
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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.
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.
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.
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PROG
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(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])
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CROSSREFS
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Cf. A352544 (half or add largest anagram), A004186 (largest anagram: arrange digits in decreasing order).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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