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A301938 Numbers n with the property that n^2 contains a sequence of four or more consecutive 8's.

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

Offset: 1

Sean Reeves, Mar 28 2018

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

			For n=1, 1609^2 = 2588881.

Robert Israel, Table of n, a(n) for n = 1..10000

filter:= n -> StringTools:-Search("8888",sprintf("%d",n^2))<> 0:
select(filter, [$1..10^5]); # Robert Israel, Mar 29 2018

More terms from Robert Israel, Mar 29 2018

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User: Sean Reeves

A301938 Numbers n with the property that n^2 contains a sequence of four or more consecutive 8's.

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