cp's OEIS Frontend

A023086 Numbers k such that k and 2*k are anagrams.

%I A023086 #43 May 22 2021 15:31:50
%S A023086 0,125874,128574,142587,142857,258714,258741,285714,285741,412587,
%T A023086 412857,425871,428571,1025874,1028574,1042587,1042857,1052874,1054287,
%U A023086 1072854,1074285,1078524,1078542,1085274,1085427,1087254,1087425,1087524,1087542
%N A023086 Numbers k such that k and 2*k are anagrams.
%C A023086 All terms are divisible by 9. - _Eric M. Schmidt_, Jul 12 2014
%C A023086 If x and y are in the sequence, then so is 10^m*x + y if y < 10^m. - _Robert Israel_, Mar 20 2017
%C A023086 From _Petros Hadjicostas_, Jul 29 2020: (Start)
%C A023086 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)).
%C A023086 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.
%C A023086 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)
%D A023086 Fred Schuh, The Master Book of Mathematical Recreations, Dover, New York, 1968, pp. 31-35.
%H A023086 David W. Wilson, <a href="/A023086/b023086.txt">Table of n, a(n) for n = 1..10001</a>
%H A023086 Mark Dominus, <a href="http://blog.plover.com/math/dd.html">When do n and 2n have the same digits?</a>
%p A023086 Res:= 0:
%p A023086 for d from 1 to 7 do
%p A023086   for n from 10^(d-1)+8 to 5*10^(d-1)-1 by 9 do
%p A023086     if sort(convert(n,base,10)) = sort(convert(2*n,base,10)) then
%p A023086       Res:= Res, n
%p A023086     fi
%p A023086 od od:
%p A023086 Res; # _Robert Israel_, Mar 20 2017
%t A023086 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 *)
%o A023086 (Python)
%o A023086 def ok(n): return sorted(str(n)) == sorted(str(2*n))
%o A023086 print(list(filter(ok, range(1087543)))) # _Michael S. Branicky_, May 21 2021
%o A023086 (Python) # use with ok above for larger terms
%o A023086 def auptod(maxd):
%o A023086   return [0] + list(filter(ok, (n for d in range(2, maxd+1) for n in range(10**(d-1)-1, 5*10**(d-1), 9))))
%o A023086 print(auptod(7)) # _Michael S. Branicky_, May 22 2021
%Y A023086 Cf. A023087, A023088, A023089, A023090, A023091, A023092, A023093, A336670.
%K A023086 nonn,base
%O A023086 1,2
%A A023086 _David W. Wilson_