A352544 a(n) = n/2 if n is even, otherwise n + A004186(n), where A004186 = arrange digits in decreasing order.

0, 2, 1, 6, 2, 10, 3, 14, 4, 18, 5, 22, 6, 44, 7, 66, 8, 88, 9, 110, 10, 42, 11, 55, 12, 77, 13, 99, 14, 121, 15, 62, 16, 66, 17, 88, 18, 110, 19, 132, 20, 82, 21, 86, 22, 99, 23, 121, 24, 143, 25, 102, 26, 106, 27, 110, 28, 132, 29, 154, 30, 122, 31, 126, 32, 130, 33, 143, 34, 165, 35, 142, 36, 146, 37, 150, 38, 154, 39, 176, 40, 162, 41, 166, 42, 170, 43, 174, 44, 187, 45

Offset: 0

Author

Eric Angelini and M. F. Hasler, Mar 20 2022

Keywords

• nonn
• base

Comments

A variant of the Collatz (3x+1) map A006370. See A352540 - A352543 for more about iterations of this map.

Links

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

Crossrefs

Cf. A004186.

Coincides with A064680 (half if even, double if odd) for n < 13.

Cf. A352540 (initial values with infinite orbit under A352544), A352541 (number of iterations of A352544 to reach a value for the second time), A352542 (orbit of 89 under A352544), A352543 (numbers that end in a loop of length > 3 under A352544), A352545 (representatives of loops of length > 3).

Programs

PARI

apply( {A352544(n)=if(n%2,n+A004186(n),n\2)}, [0..90]) \\ with A004186(n)=fromdigits(vecsort(digits(n),,4))