wu :: forums « wu :: forums - Curious numbers » Welcome, Guest. Please Login or Register. May 19th, 2024, 10:09am RIDDLES SITE WRITE MATH! Home Help Search Members Login Register
 wu :: forums    riddles    cs (Moderators: Eigenray, towr, william wu, Grimbal, ThudnBlunder, SMQ, Icarus)    Curious numbers « Previous topic | Next topic »
 Pages: 1 Reply Notify of replies Send Topic Print
 Author Topic: Curious numbers  (Read 695 times)
FiBsTeR
Senior Riddler

Gender:
Posts: 581
 Curious numbers   « on: Jul 7th, 2018, 6:26am » Quote Modify

A k-curious number is a positive integer s such that when you multiply s by k, you get s except with the right-most digit moved to the left.

For example, the smallest 4-curious number is 102564 because:
102564 * 4 = 410256

The smallest 5-curious number is 142857 because:
142857 * 5 = 714285

What is the smallest 6-curious number?
 IP Logged
towr
wu::riddles Moderator
Uberpuzzler

Some people are average, some are just mean.

Gender:
Posts: 13730
 Re: Curious numbers   « Reply #1 on: Jul 7th, 2018, 12:23pm » Quote Modify

It seems to be 1016949152542372881355932203389830508474576271186440677966

Say we're trying to find the number N = 10M+D where D is a digit and M a natural number
We want 6*(10M+D) = D*10^K + M, where K is the number of digits in M
Simplify this to 59*M = (10^K-6)*D
And now you can do a much more targeted search than running through every number: D is limited to 9 choices, and we can just try increasing K

#python-code
for K in range(100):
for D in range(1,10):
X = (10**K-6)*D
if X % 59 == 0:
M = X//59
if len(str(10*M+D)) == len(str(D*10**K + M)):
print((10*M+D), '-', D*10**K + M)
 « Last Edit: Jul 7th, 2018, 12:25pm by towr » IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
towr
wu::riddles Moderator
Uberpuzzler

Some people are average, some are just mean.

Gender:
Posts: 13730
 Re: Curious numbers   « Reply #2 on: Jul 7th, 2018, 12:32pm » Quote Modify

Wikipedia calls these parasitic numbers
 IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
FiBsTeR
Senior Riddler

Gender:
Posts: 581
 Re: Curious numbers   « Reply #3 on: Jul 9th, 2018, 7:34am » Quote Modify

Nice, that's right!
 IP Logged
 Pages: 1 Reply Notify of replies Send Topic Print

 Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft => cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »