A301938 - OEIS

%I #20 Nov 04 2020 11:01:02

%S 1609,6992,9428,10094,12202,16090,16667,16849,20221,20359,21187,22917,

%T 24267,25197,27083,29641,29813,29814,31763,33333,35901,39101,41096,

%U 41664,43461,48391,50298,51609,53748,62361,66667,69920,70359,72594,72917,73409,74087,76019,76739,77083,79641,82999,83333

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

%C 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.

%C 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

%H Robert Israel, <a href="/A301938/b301938.txt">Table of n, a(n) for n = 1..10000</a>

%e For n=1, 1609^2 = 2588881.

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

%p select(filter, [$1..10^5]); # _Robert Israel_, Mar 29 2018

%K nonn,base

%O 1,1

%A _Sean Reeves_, Mar 28 2018

%E More terms from _Robert Israel_, Mar 29 2018