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A023086 Numbers n such that n and 2*n are anagrams. 15
0, 125874, 128574, 142587, 142857, 258714, 258741, 285714, 285741, 412587, 412857, 425871, 428571, 1025874, 1028574, 1042587, 1042857, 1052874, 1054287, 1072854, 1074285, 1078524, 1078542, 1085274, 1085427, 1087254, 1087425, 1087524, 1087542 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All terms are divisible by 9. - Eric M. Schmidt, Jul 12 2014

If x and y are in the sequence, then so is 10^k*x + y if y < 10^k. - Robert Israel, Mar 20 2017

From Petros Hadjicostas, Jul 29 2020: (Start)

This is Schuh's (1968) "doubles puzzle" (the double of k is 2*k). On five pages of his book, he finds the twelve 6-digit numbers that belong to this sequence (a(2) to a(13)) and the 288 7-digit numbers of the sequence (a(14) to a(301)).

All numbers in this sequence are permutations of numbers that are combinations of numbers from A336670, which is related to another puzzle of Schuh (1968). Before he solved this puzzle, he had to solve the puzzle described in A336670.

For example, a(2) = 125874 through a(13) = 428571 are all permutations of the number 512874, which is a combination of the numbers 512 and 874 that appear in A336670. (End)

REFERENCES

Fred Schuh, The Master Book of Mathematical Recreations, Dover, New York, 1968, pp. 31-35.

LINKS

David W. Wilson, Table of n, a(n) for n = 1..10001

Mark Dominus, When do n and 2n have the same digits?

MAPLE

Res:= 0:

for d from 1 to 7 do

  for n from 10^(d-1)+8 to 5*10^(d-1)-1 by 9 do

    if sort(convert(n, base, 10)) = sort(convert(2*n, base, 10)) then

      Res:= Res, n

    fi

od od:

Res; # Robert Israel, Mar 20 2017

MATHEMATICA

si[n_] := Sort@ IntegerDigits@ n; Flatten@ {0, Table[ Select[ Range[ 10^e+8, 5*10^e-1, 9], si[#] == si[2 #] &], {e, 6}]} (* Giovanni Resta, Mar 20 2017 *)

CROSSREFS

Cf. A023087, A023088, A023089, A023090, A023091, A023092, A023093, A336670.

Sequence in context: A252208 A175691 A133220 * A230722 A251016 A251027

Adjacent sequences:  A023083 A023084 A023085 * A023087 A023088 A023089

KEYWORD

nonn,base

AUTHOR

David W. Wilson

STATUS

approved

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Last modified April 10 23:13 EDT 2021. Contains 342877 sequences. (Running on oeis4.)