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A145491
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In these bases, there exist numbers written with only one distinct digit whose translation in binary is also written with the same lonely digit.
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0
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5, 6, 14, 30, 62, 90, 126, 254, 510, 1022, 2046, 4094, 8190
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OFFSET
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1,1
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COMMENTS
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All terms are equal to 2^n-2, except 5 and 90.
In base 2^n-2, we need 2 digits when there are n digits in binary.
In base 5, we need 3 digits for 5 digits in binary.
In base 90, we need 3 digits for 13 digits in binary.
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LINKS
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EXAMPLE
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In base 5 : 11111[2] = 111[5].
In base 90 : 1111111111111[2] = 111[90].
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PROG
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(Python) from math import *
.for b1 in range(2, 3):
....for b2 in range(b1+1, 10001):
........for m in range(2, 20):
............for n in range(2, m+1):
................if (1-b1**m)*(1-b2)==(1-b1)*(1-b2**n):
....................print "b1, b2=", b1, b2, " m, n=", m, n
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CROSSREFS
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KEYWORD
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base,nonn,more
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AUTHOR
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STATUS
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approved
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