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A159754 Numbers n with property that n^2 ends with 81. 3

%I

%S 9,41,59,91,109,141,159,191,209,241,259,291,309,341,359,391,409,441,

%T 459,491,509,541,559,591,609,641,659,691,709,741,759,791,809,841,859,

%U 891,909,941,959,991,1009,1041,1059,1091,1109,1141,1159,1191,1209,1241,1259

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

%C First 9 terms = 9th row in A111445.

%H Alois P. Heinz, <a href="/A159754/b159754.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F a(1) = 9, a(2) = 41, a(n) = a(n-2)+50, n=3,4,...

%F a(n) = (1/2)*(50*n-25+7*(-1)^n), n=1,2,...

%F a(n) = a(n-1)+a(n-2)-a(n-3). G.f.: x*(9*x^2+32*x+9) / ((x-1)^2*(x+1)). - _Colin Barker_, Jul 04 2014

%p a:= n-> iquo(n-1, 2, 'r')*50 +[9, 41][r+1]:

%p seq(a(n), n=1..60); # _Alois P. Heinz_, Dec 07 2016

%t Select[Range[1300],PowerMod[#,2,100]==81&] (* or *) LinearRecurrence[{1,1,-1},{9,41,59},60] (* _Harvey P. Dale_, May 17 2018 *)

%o (PARI) select(n->n^2%100==81, vector(10^3,n,n)) \\ _Colin Barker_, Jul 04 2014

%Y 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 nonn,base,easy

%O 1,1

%A _Zak Seidov_, Apr 21 2009

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Last modified July 22 16:24 EDT 2019. Contains 325224 sequences. (Running on oeis4.)