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%I #16 Mar 14 2018 04:38:05
%S 1,2413,3142,25314,41352,28463517,28536417,34872156,35827146,43781265,
%T 46281735,53718264,56218734,64172853,65127843,71463582,71536482
%N Given a number n with k digits, enumerate the positions of the digits starting from LSD = 1 to MSD = k. Then concatenate in ascending order the positions of the minimum digit in n. Repeat the same process for all the different digits, in ascending order, in n. Sequence lists the fixed points of this transform.
%C If x is in the sequence, then the digit reversal of x also belongs to the sequence.
%C If we consider the numbers that under this transform produce a multiple of the number itself, for n <= 10^8 we should add only 153363. Digit 1 is in position 6, 3 in position 1, 3 and 4, 5 in position 5, 6 in position 2. Finally, 613452 / 153363 = 4.
%e In 2413, digit 1 is in position 2, 2 in position 4, 3 in position 1, 4 in position 3. Therefore concat(2,4,1,3) = 2413 that is a fixed point.
%e In 56218734 digit 1 is in position 5, 2 in position 6, 3 in position 2, 4 in position 1, 5 in position 8, 6 in position 7, 7 in position 3, 8 in position 4. Therefore concat(5,6,2,1,8,7,3,4) = 56218734 that is a fixed point.
%p with(numtheory):P:=proc(q) local a,b,j,k,n;
%p for n from 1 to q do a:=convert(n,base,10); b:=0;
%p for k from 0 to 9 do for j from 1 to nops(a) do
%p if a[j]=k then b:=b*10+j; fi; od;
%p od; if b=n then print(n); fi; od; end: P(10^9);
%Y Cf. A260275, A260385, A260386.
%K nonn,base,fini
%O 1,2
%A _Paolo P. Lava_, Jul 24 2015
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