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Let s(n) = s_3(n) be digit sum of n in base 3. Consider iterations: a_1(n) = s(2^n), a_2(n) = s(2^n+a_1(n)),a_3(n)=s(2^n+a_2(n)),...The sequence lists those n for which these iterations are (eventually) periodic with period > 1.
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%I #13 Feb 13 2013 23:58:28

%S 5,7,8,17,21,23,26,31,39,40,41,45,49,51,52,53,58,62,64,67,69,78,81,82,

%T 84,87,91,93,108,113,115,116,119,121,122,128,131,135,136,139,142,151,

%U 152,155,163,170,173,174,178,181,191,193,195,198,201

%N Let s(n) = s_3(n) be digit sum of n in base 3. Consider iterations: a_1(n) = s(2^n), a_2(n) = s(2^n+a_1(n)),a_3(n)=s(2^n+a_2(n)),...The sequence lists those n for which these iterations are (eventually) periodic with period > 1.

%C For every number n which is not in the sequences, there exists N=N(n) such that, for k>N, a_k(n)=constant(k).

%F Enlarged on 1 numbers which are not in A169655.

%Y Cf. A053735, A000079.

%K nonn,base

%O 1,1

%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Apr 06 2012