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

1,1

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

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

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

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