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A007496
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Numbers n such that the decimal expansions of 2^n and 5^n contain no 0's (probably 33 is last term).
(Formerly M0497)
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28
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0, 1, 2, 3, 4, 5, 6, 7, 9, 18, 33
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OFFSET
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1,3
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COMMENTS
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Equivalently, numbers n such that 10^n is the product of two integers without any zero digits.
10^0 = 1 * 1
10^1 = 2 * 5
10^2 = 4 * 25
10^3 = 8 * 125
10^4 = 16 * 625
10^5 = 32 * 3125
10^6 = 64 * 15625
10^7 = 128 * 78125
10^9 = 512 * 1953125
10^18 = 262144 * 3814697265625
10^33 = 8589934592 * 116415321826934814453125. (End)
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REFERENCES
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J. S. Madachy, Madachy's Mathematical Recreation, "#2. Number Toughies", pp. 126-8, Dover NY 1979.
C. S. Ogilvy and J. T. Anderson, Excursions in Number Theory. Oxford Univ. Press, 1966, p. 89.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MAPLE
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q:= n-> andmap(t-> not 0 in convert(t, base, 10), [2^n, 5^n]):
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MATHEMATICA
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Range@(10^5) // Select[Last@DigitCount@(5^#) == 0 &] // Select[Last@DigitCount@(2^#) == 0 &] (* Hans Rudolf Widmer, Feb 02 2022 *)
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PROG
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(PARI) isok(n) = vecmin(digits(2^n)) && vecmin(digits(5^n)); \\ Michel Marcus, Dec 28 2015
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CROSSREFS
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KEYWORD
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fini,nonn,full,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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