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A301938 Numbers n with the property that n^2 contains a sequence of four or more consecutive 8's. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..43.

EXAMPLE

For n=1, 1609^2 = 2588881.

MAPLE

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

select(filter, [$1..10^5]); # Robert Israel, Mar 29 2018

CROSSREFS

Sequence in context: A064251 A238149 A023685 * A205832 A317397 A236060

Adjacent sequences:  A301935 A301936 A301937 * A301939 A301940 A301941

KEYWORD

nonn,base

AUTHOR

Sean Reeves, Mar 28 2018

EXTENSIONS

More terms from Robert Israel, Mar 29 2018

STATUS

approved

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Last modified January 22 07:39 EST 2020. Contains 331139 sequences. (Running on oeis4.)