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%I #3 Oct 27 2023 22:00:46
%S 1,3,6,9,10,12,15,18,21,30,39,45,48,51,60,90,100,102,105,111,120,150,
%T 180,201,210,249,300,318,321,348,351,390,450,480,501,510,549,600,900,
%U 1000,1002,1005,1011,1020,1050,1101,1110,1149,1200,1500,1761,1800,2001
%N Numbers n such that the iterative cycle: n -> sum of digits of n^2 has only one distinct element.
%C 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.
%e 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 ...
%Y Cf. A007953, A004159, A061903 - A061910.
%K nonn,base
%O 1,2
%A _Asher Auel_, May 17 2001
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