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

9, 41, 59, 91, 109, 141, 159, 191, 209, 241, 259, 291, 309, 341, 359, 391, 409, 441, 459, 491, 509, 541, 559, 591, 609, 641, 659, 691, 709, 741, 759, 791, 809, 841, 859, 891, 909, 941, 959, 991, 1009, 1041, 1059, 1091, 1109, 1141, 1159, 1191, 1209, 1241, 1259

Offset

1,1

Comments

First 9 terms = 9th row in A111445.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

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

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

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

Maple

a:= n-> iquo(n-1, 2, 'r')*50 +[9, 41][r+1]:
seq(a(n), n=1..60);  # Alois P. Heinz, Dec 07 2016

Mathematica

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

Prog

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

Crossrefs

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.

Sequence in context: A093469 A120932 A034925 * A045804 A322055 A198943

Adjacent sequences: A159751 A159752 A159753 * A159755 A159756 A159757

Keyword

nonn,base,easy

Author

Zak Seidov, Apr 21 2009

Status

approved