

A145461


Numbers that can be written with a single digit in base 10 as well as in some base b<10.


1



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 777
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OFFSET

1,3


COMMENTS

If a number is written in base 10 with a digit x and in base b with a digit y, then (b1)*x*10^n  9*y*b^m + (9*y  (b1)*x) = 0. Varying parameters b=2,3,...,9; x=1,2,...,9; and y=1,2,...,b1 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)


LINKS

Table of n, a(n) for n=1..11.


EXAMPLE

777[base 10]=3333[base 6]


PROG

(Python) from math import *
.i=1 while i<(10**10001)/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


CROSSREFS

Sequence in context: A124107 A257275 A112014 * A075154 A187924 A070938
Adjacent sequences: A145458 A145459 A145460 * A145462 A145463 A145464


KEYWORD

base,nonn,full,fini


AUTHOR

Sébastien Dumortier, Oct 10 2008


EXTENSIONS

Completeness and finiteness established by Max Alekseyev, Nov 06 2008


STATUS

approved



