login
A061904
Numbers n such that the iterative cycle: n -> sum of digits of n^2 has only one distinct element.
1
1, 3, 6, 9, 10, 12, 15, 18, 21, 30, 39, 45, 48, 51, 60, 90, 100, 102, 105, 111, 120, 150, 180, 201, 210, 249, 300, 318, 321, 348, 351, 390, 450, 480, 501, 510, 549, 600, 900, 1000, 1002, 1005, 1011, 1020, 1050, 1101, 1110, 1149, 1200, 1500, 1761, 1800, 2001
OFFSET
1,2
COMMENTS
Since the only numbers invariant under this iteration are 1 and 9, n is contained in this sequence iff the sum of digits of n^2 is 1 or 9.
EXAMPLE
6 -> 3+6 = 9 -> 8+1 = 9 thus 9 is the only element of the iterative cycle of 6. 12 -> 1+4+4 = 9 -> 8+1 = 9 ...
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Asher Auel, May 17 2001
STATUS
approved