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

0,2

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.

Links

Table of n, a(n) for n=0..90.

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

Formula

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

Example

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.

Prog

(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])

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).

Sequence in context: A187184 A301375 A325273 * A359438 A279408 A135592

Adjacent sequences: A352538 A352539 A352540 * A352542 A352543 A352544

Keyword

nonn,base

Author

M. F. Hasler, Mar 20 2022

Status

approved