login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A023086 Numbers k such that k and 2*k are anagrams. 17
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^m*x + y if y < 10^m. - 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
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 *)
PROG
(Python)
def ok(n): return sorted(str(n)) == sorted(str(2*n))
print(list(filter(ok, range(1087543)))) # Michael S. Branicky, May 21 2021
(Python) # use with ok above for larger terms
def auptod(maxd):
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))))
print(auptod(7)) # Michael S. Branicky, May 22 2021
CROSSREFS
Sequence in context: A252208 A175691 A133220 * A230722 A251016 A349284
KEYWORD
nonn,base
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)