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A275218 Numbers in 2-cycles of RATS sequences. 0
78, 117, 156, 288, 11127, 11667, 23388, 27888, 111177, 228888, 111111777, 222888888, 1111122267, 3333337788, 111111117777, 222288888888, 111111111177777, 222228888888888, 111111111111777777, 222222888888888888 (list; graph; refs; listen; history; text; internal format)



Numbers n such that A036839(A036839(n)) = n.

Subset of A161596.

Contains A002275(3*k) + 6*A002275(k) and 2*A002275(3*k)+6*A002275(2*k) for all k>0.

In particular, this sequence and A161596 are infinite.

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)?


Table of n, a(n) for n=1..20.


78 is in the sequence because A036839(78) = 156 and A036839(156) = 78.


rev:= proc(n) local t, L;

   L:= convert(n, base, 10);

   add(10^j*L[-1-j], j=0..nops(L)-1)

end proc:

sord:= proc(n) local L, t;

  L:= sort(convert(n, base, 10), `>`);

  add(10^j*L[1+j], j=0..nops(L)-1)

end proc:

rats:= proc(n) option remember;  sord(n + rev(n)) end proc:

Res:= NULL:

for d from 1 to 15 do

  for x1 from 0 to d do

    for x2 from 0 to d-x1 do

      for x3 from 0 to d-x1-x2 do

         for x4 from 0 to d-x1-x2-x3 do

           for x5 from 0 to d-x1-x2-x3-x4 do

             for x6 from 0 to d-x1-x2-x3-x4-x5 do

               for x7 from 0 to d-x1-x2-x3-x4-x5-x6 do

                 for x8 from 0 to d-x1-x2-x3-x4-x5-x6-x7 do

                   x9:= d-x1-x2-x3-x4-x5-x6-x7-x8;

                   L:= [1$x1, 2$x2, 3$x3, 4$x4, 5$x5, 6$x6, 7$x7, 8$x8, 9$x9];

                   x:= add(L[-i]*10^(i-1), i=1..d);

                   if rats(rats(x)) = x then Res:= Res, x fi

od od od od od od od od od:



Cf. A002275, A036839, A161596.

Sequence in context: A157355 A224666 A161596 * A260364 A185077 A042945

Adjacent sequences:  A275215 A275216 A275217 * A275219 A275220 A275221




Robert Israel, Jul 20 2016



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Last modified April 14 19:16 EDT 2021. Contains 342951 sequences. (Running on oeis4.)