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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 (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
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 * A352545 A205832 A317397
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 March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)