A260274 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.

1, 2413, 3142, 25314, 41352, 28463517, 28536417, 34872156, 35827146, 43781265, 46281735, 53718264, 56218734, 64172853, 65127843, 71463582, 71536482

Offset

1,2

Comments

If x is in the sequence, then the digit reversal of x also belongs to the sequence.

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.

Links

Table of n, a(n) for n=1..17.

Example

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.
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.

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 0 to 9 do for j from 1 to nops(a) do
if a[j]=k then b:=b*10+j; fi; od;
od; if b=n then print(n); fi; od; end: P(10^9);

Crossrefs

Cf. A260275, A260385, A260386.

Sequence in context: A236038 A323271 A283783 * A234126 A159346 A256835

Adjacent sequences: A260271 A260272 A260273 * A260275 A260276 A260277

Keyword

nonn,base,fini

Author

Paolo P. Lava, Jul 24 2015

Status

approved