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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 (list; graph; refs; listen; history; internal format)
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

Cf. A007953, A004159, A061903 - A061910.

Sequence in context: A133006 A055264 A113502 * A206284 A188299 A187577

Adjacent sequences:  A061901 A061902 A061903 * A061905 A061906 A061907

KEYWORD

nonn,base

AUTHOR

Asher Auel (asher.auel(AT)reed.edu), May 17 2001

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Last modified February 16 21:51 EST 2012. Contains 205978 sequences.