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%I #22 Jul 21 2016 02:48:57
%S 78,117,156,288,11127,11667,23388,27888,111177,228888,111111777,
%T 222888888,1111122267,3333337788,111111117777,222288888888,
%U 111111111177777,222228888888888,111111111111777777,222222888888888888
%N Numbers in 2-cycles of RATS sequences.
%C Numbers n such that A036839(A036839(n)) = n.
%C Subset of A161596.
%C Contains A002275(3*k) + 6*A002275(k) and 2*A002275(3*k)+6*A002275(2*k) for all k>0.
%C In particular, this sequence and A161596 are infinite.
%C Do all sufficiently large members of the sequence have the form A002275(3*k) + 6*A002275(k) or 2*A002275(3*k)+6*A002275(2*k)?
%e 78 is in the sequence because A036839(78) = 156 and A036839(156) = 78.
%p rev:= proc(n) local t,L;
%p L:= convert(n,base,10);
%p add(10^j*L[-1-j],j=0..nops(L)-1)
%p end proc:
%p sord:= proc(n) local L,t;
%p L:= sort(convert(n,base,10),`>`);
%p add(10^j*L[1+j],j=0..nops(L)-1)
%p end proc:
%p rats:= proc(n) option remember; sord(n + rev(n)) end proc:
%p Res:= NULL:
%p for d from 1 to 15 do
%p for x1 from 0 to d do
%p for x2 from 0 to d-x1 do
%p for x3 from 0 to d-x1-x2 do
%p for x4 from 0 to d-x1-x2-x3 do
%p for x5 from 0 to d-x1-x2-x3-x4 do
%p for x6 from 0 to d-x1-x2-x3-x4-x5 do
%p for x7 from 0 to d-x1-x2-x3-x4-x5-x6 do
%p for x8 from 0 to d-x1-x2-x3-x4-x5-x6-x7 do
%p x9:= d-x1-x2-x3-x4-x5-x6-x7-x8;
%p L:= [1$x1,2$x2,3$x3,4$x4,5$x5,6$x6,7$x7,8$x8,9$x9];
%p x:= add(L[-i]*10^(i-1),i=1..d);
%p if rats(rats(x)) = x then Res:= Res,x fi
%p od od od od od od od od od:
%p sort([Res]);
%Y Cf. A002275, A036839, A161596.
%K nonn,base
%O 1,1
%A _Robert Israel_, Jul 20 2016
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