The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A139285

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A139285

Smallest nontrivial number m that when expressed in base n and then interpreted in base 10, is a multiple of the original number.
(history; published version)

#45 by Alois P. Heinz at Sat Nov 09 19:31:56 EST 2024

STATUS

proposed

approved

#44 by Robert C. Lyons at Sat Nov 09 19:31:37 EST 2024

STATUS

editing

proposed

#43 by Robert C. Lyons at Sat Nov 09 19:31:34 EST 2024

COMMENTS

Note that for n=1, the unitary numeral system is used, whereas for n>=2, it is the usual base-dependant dependent positional numeral system. - Michel Marcus, Sep 16 2020

STATUS

approved

editing

#42 by Sean A. Irvine at Fri Oct 23 15:13:26 EDT 2020

STATUS

proposed

approved

#41 by Dimiter Skordev at Mon Sep 28 07:30:25 EDT 2020

STATUS

editing

proposed

Discussion

Mon Sep 28

15:33

Michel Marcus: for n in range(2, 10): should rather be for n in range(2, 9)  ??

Tue Sep 29

02:51

Dimiter Skordev: In Python, 2 belongs to the set range(2,9), but 9 does not belong to it.

#40 by Dimiter Skordev at Mon Sep 28 07:10:05 EDT 2020

EXAMPLE

a(1)=3 since 3 in base 1 ('unary') is 111 and , interpreted in base 10, 111 is a number divisible by 3, whereas 2 in base 1 is 11 and, interpreted in base 10, 11 is not divisible by 2.

a(3)=7 since 7 in base 3 is 21 and , interpreted in base 10, 21 is divisible by 7, whereas 3, 4, 5, 6 in base 3 are, respectively, 10, 11, 12, 20 and, interpreted in base 10, these are numbers not divisible, respectively, by 3, 4, 5, 6.

PROG

m, M, d, e=n, 10, 10-n, n-1

m=m+1

while u%n==e0:

m, M=m+1, M+1+s

# Dimiter Skordev, Sep 26 28 2020

STATUS

proposed

editing

Discussion

Mon Sep 28

07:27

Dimiter Skordev: I corrected a mistake in the example section (the divisibility of 21  by 7 must be indicated instead of the divisibility of 21 by 3), and I added the missing reasoning concerning the minimality. I slightly modified the Python program, thus shortening a little its run time.

#39 by Joerg Arndt at Sat Sep 26 07:30:36 EDT 2020

STATUS

editing

proposed

#38 by Joerg Arndt at Sat Sep 26 07:30:30 EDT 2020

LINKS

Dimiter Skordev, <a href="/A139285/a139285.py.txt">Python script</a>

Dimiter Skordev, <a href="/A139285/a139285_1.py.txt">Python script</a>

PROG

# _Dimiter Skordev, _, Sep 26 2020

STATUS

proposed

editing

#37 by Dimiter Skordev at Sat Sep 26 07:18:05 EDT 2020

STATUS

editing

proposed

#36 by Dimiter Skordev at Sat Sep 26 07:17:07 EDT 2020

PROG

~

# Dimiter Skordev, Sep 26 2020