A159775 - OEIS

%I #10 Jan 02 2018 15:45:55

%S 9,2859,9009,9041,28491,28509,28541,28559,28591,28609,90009,90041,

%T 90059,90091,90109,90141,90159,90191,90209,90241,90259,90291,90309,

%U 90341,90359,90391,90409,90441,90459,90491,90509,90541,284609,284641,284659

%N Numbers n with property that n^2 starts and ends with 81.

%C Most first differences are alternatively 18 and 32.

%H Robert Israel, <a href="/A159775/b159775.txt">Table of n, a(n) for n = 1..10000</a>

%e map(x-> x^2, {9,2859,9009,9041,28491}) = {81,8173881,81162081,81739681,811737081}.

%p f:= proc(d) local L,U,a,b;

%p L:= ceil(sqrt(81*10^(d-2)));

%p U:= floor(sqrt(82*10^(d-2)));

%p op(select(t -> t >= L and t <= U, [seq(seq(100*a+b, b=[9,41,59,91]),a=ceil((L-91)/100)..floor((U-4)/100))]))

%p end proc:

%p seq(f(d),d=2..12); # _Robert Israel_, Jan 02 2018

%t be9Q[n_]:=Module[{idn=IntegerDigits[n^2]},Take[idn,2]== Take[idn,-2] =={8,1}]; nn=300000;Sort[Join[Select[Range[9,nn,10],be9Q], Select[Range[ 11,nn,10],be9Q]]] (* _Harvey P. Dale_, Apr 30 2011 *)

%Y A159754 Numbers n with property that n^2 ends with 81. A159254 Numbers n with property that n^2 ends with 49. A111445 n-th row contains first n numbers whose squares end in n^2.

%K base,nonn

%O 1,1

%A _Zak Seidov_, Apr 21 2009