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A145461
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Numbers that can be written with a single digit in base 10 as well as in some base b<10.
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1
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 777
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| If a number is written in base 10 with a digit x and in base b with a digit y, then (b-1)*x*10^n - 9*y*b^m + (9*y - (b-1)*x) = 0. Varying parameters b=2,3,...,9; x=1,2,...,9; and y=1,2,...,b-1 give a finite number of equations. It is easy to find all solutions (w.r.t. n and m) of each equation or establish that there are none. In particular, for b=7, x=9, y=5, the equation is 54*10^n - 45*7^m - 9 = 0 or 6*10^n - 5*7^m - 1 = 0 that does not have solutions since the left hand side is not 0 modulo 5. (Alekseyev)
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EXAMPLE
| 777[base 10]=3333[base 6]
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PROG
| (Python) from math import *
.i=1 while i<(10**1000-1)/9:
....i=10*i+1
....for m in range(1, 10):
........q=i*m
........q2=q
........for b in range(2, 10):
............restes=[]
............q=q2
............while q>0:
................r=q%b
................q=q/b
................restes.append(r)
............if restes==[restes[0]]*len(restes):
................print q2, restes, "en base ", b
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CROSSREFS
| Sequence in context: A069747 A124107 A112014 * A075154 A187924 A070938
Adjacent sequences: A145458 A145459 A145460 * A145462 A145463 A145464
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KEYWORD
| base,nonn,full,fini
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AUTHOR
| Sebastien Dumortier (sdumortier(AT)ac-limoges.fr), Oct 10 2008
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EXTENSIONS
| Completeness and finiteness established by Max Alekseyev (maxale(AT)gmail.com), Nov 06 2008
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