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

1,2

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.

Links

Table of n, a(n) for n=1..53.

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

Cf. A007953, A004159, A061903 - A061910.

Sequence in context: A113502 A229307 A356453 * A206284 A372850 A363950

Adjacent sequences: A061901 A061902 A061903 * A061905 A061906 A061907

Keyword

nonn,base

Author

Asher Auel, May 17 2001

Status

approved