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A301938
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Numbers n with the property that n^2 contains a sequence of four or more consecutive 8's.
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1
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1609, 6992, 9428, 10094, 12202, 16090, 16667, 16849, 20221, 20359, 21187, 22917, 24267, 25197, 27083, 29641, 29813, 29814, 31763, 33333, 35901, 39101, 41096, 41664, 43461, 48391, 50298, 51609, 53748, 62361, 66667, 69920, 70359, 72594, 72917, 73409, 74087, 76019, 76739, 77083, 79641, 82999, 83333
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OFFSET
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1,1
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COMMENTS
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The sequence would certainly be infinite and runs of more than four 8's occur relatively frequently. For example, between 1 and 26000, there are two numbers whose squares contain five sequential 8's. These are 12202^2 = 148888804 and 20221^2 = 408888841.
If n is in the sequence, then so are k*10^d+n for all k >= 1, where n^2 has d digits. Therefore the sequence has nonzero lower asymptotic density. Presumably the asymptotic density is 1. - Robert Israel, Mar 29 2018
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LINKS
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EXAMPLE
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For n=1, 1609^2 = 2588881.
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MAPLE
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filter:= n -> StringTools:-Search("8888", sprintf("%d", n^2))<> 0:
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CROSSREFS
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KEYWORD
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nonn,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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