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.

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

Offset: 0

Author

M. F. Hasler, Mar 20 2022

Keywords

• nonn
• base

Comments

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.

Examples

			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.
		

Links

• Eric Angelini, Divide by 2 or add the biggest anagram, math-fun discussion list, Mar 20 2022

Crossrefs

Cf. A352544 (half or add largest anagram), A004186 (largest anagram: arrange digits in decreasing order).

Cf. A352542 (trajectory of 89 under A352544), A352540 (indices of zeros).

Programs

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])

Formula

a(n) = 0 iff n is in A352540.