A275218 Numbers in 2-cycles of RATS sequences.

78, 117, 156, 288, 11127, 11667, 23388, 27888, 111177, 228888, 111111777, 222888888, 1111122267, 3333337788, 111111117777, 222288888888, 111111111177777, 222228888888888, 111111111111777777, 222222888888888888

Offset: 1

Author

Robert Israel, Jul 20 2016

Keywords

• nonn
• base

Comments

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)?

Examples

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

Crossrefs

Cf. A002275, A036839, A161596.

Programs

Maple

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:
sort([Res]);