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A071531
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Smallest exponent r such that n^r contains a zero digit (in base 10).
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0
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10, 10, 5, 8, 9, 4, 4, 5, 1, 5, 4, 6, 7, 4, 3, 7, 4, 4, 1, 5, 3, 6, 6, 4, 6, 5, 5, 4, 1, 6, 2, 2, 3, 4, 5, 3, 4, 5, 1, 5, 3, 3, 4, 2, 5, 2, 2, 2, 1, 2, 2, 2, 4, 2, 5, 4, 6, 3, 1, 5, 6, 3, 2, 4, 6, 3, 9, 3, 1, 2, 6, 3, 3, 4, 8, 4, 2, 3, 1, 4, 5, 5, 2, 4, 3, 3, 6, 3, 1, 5, 5, 3, 3, 2, 7, 2, 2, 2, 1, 1, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Does r always exist? Is it bounded? Is 10 an upper bound?
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EXAMPLE
| a(4)=5 because 4^1=4, 4^2=16, 4^3=64, 4^4=256, 4^5=1024 (has zero digit)
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PROG
| # Python (2.4) program from Tim Peters, May 19 2005. (Change leading dots to blanks.)
.def has_zero_digit(x):
.... while x:
........ x, r = divmod(x, 10)
........ if r == 0:
............ return True
.... return False
.def a(n):
.... r, p = 1, n
.... while 1:
........ if has_zero_digit(p):
............ return r
........ r += 1
........ p *= n
.for n in xrange(2, 1000000):
.... print n, a(n)
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CROSSREFS
| Sequence in context: A038311 A034078 A180011 * A112120 A099401 A087028
Adjacent sequences: A071528 A071529 A071530 * A071532 A071533 A071534
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KEYWORD
| base,nonn
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AUTHOR
| Paul Stoeber (paul.stoeber(AT)stud.tu-ilmenau.de), Jun 02 2002
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