

A260275


Fixed points of the function A260529(n) = concatenation of the positions of digits 9, 8,..., 0 in the decimal representation of n, using 1 for the rightmost digit etc., skipping digits which don't occur.


6



1, 12, 21, 123, 231, 312, 321, 1234, 1324, 2143, 2341, 3412, 3421, 4123, 4231, 4312, 4321, 12345, 13425, 14235, 14325, 21354, 23451, 24153, 24351, 31524, 32541, 34512, 34521, 45123, 45231, 45312, 45321, 51234, 51324, 52143, 52341, 53412, 53421, 54123, 54231, 54312
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OFFSET

1,2


COMMENTS

Given a number n with k digits, label the positions of the digits starting from LSD = 1 to MSD = k. Then concatenate in ascending order the positions of the maximum digit in n. Repeat the same process for all the different digits, in descending order. Sequence lists the fixed points of this transform.
If we consider the numbers that under this transform produce a multiple of the number itself, for n<= 10^9 we should add only 11780892. This has digit 9 is in position 2, 8 in positions 3 and 5, 7 in position 6, 2 in position 1, 1 in positions 7 and 8, 0 in position 4. Finally, 23561784 / 11780892 = 2.


LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..3735


EXAMPLE

In 2341 digit 4 is in position 2, 3 in position 3, 2 in position 4, 1 in position 1. Therefore concat(2,3,4,1) = 2341 that is a fixed point.
In 53412 digit 5 is in position 5, 4 in position 3, 3 in position 4, 2 in position 1, 1 in position 2. Therefore concat(5,3,4,1,2) = 53412 that is a fixed point.


MAPLE

with(numtheory): P:=proc(q) local a, b, j, k, n;
for n from 1 to q do a:=convert(n, base, 10); b:=0;
for k from 9 by 1 to 0 do for j from 1 to nops(a) do
if a[j]=k then b:=b*10^(ilog10(j)+1)+j; fi; od;
od; if type(b/n, integer) then print(n); fi;
od; end: P(10^10);


CROSSREFS

Cf. A260275, A260385, A260386.
Sequence in context: A134514 A030299 A268532 * A001292 A292523 A162391
Adjacent sequences: A260272 A260273 A260274 * A260276 A260277 A260278


KEYWORD

nonn,base,fini


AUTHOR

Paolo P. Lava, Jul 24 2015


STATUS

approved



