

A301938


Numbers n with the property that n^2 contains a sequence of four or more consecutive 8's.


1



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

1,1


COMMENTS

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


LINKS



EXAMPLE

For n=1, 1609^2 = 2588881.


MAPLE

filter:= n > StringTools:Search("8888", sprintf("%d", n^2))<> 0:


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



