A061904 Numbers n such that the iterative cycle: n -> sum of digits of n^2 has only one distinct element.

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

Author

Asher Auel, May 17 2001

Keywords

• nonn
• base

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.

Examples

			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

Cf. A007953, A004159, A061903 - A061910.