A159775 Numbers n with property that n^2 starts and ends with 81.

9, 2859, 9009, 9041, 28491, 28509, 28541, 28559, 28591, 28609, 90009, 90041, 90059, 90091, 90109, 90141, 90159, 90191, 90209, 90241, 90259, 90291, 90309, 90341, 90359, 90391, 90409, 90441, 90459, 90491, 90509, 90541, 284609, 284641, 284659

Offset

1,1

Comments

Most first differences are alternatively 18 and 32.

Links

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

Example

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

Maple

f:= proc(d) local L, U, a, b;
L:= ceil(sqrt(81*10^(d-2)));
U:= floor(sqrt(82*10^(d-2)));
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))]))
end proc:
seq(f(d), d=2..12); # Robert Israel, Jan 02 2018

Mathematica

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 *)

Crossrefs

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.

Sequence in context: A033997 A068729 A321282 * A281538 A335010 A203744

Adjacent sequences: A159772 A159773 A159774 * A159776 A159777 A159778

Keyword

base,nonn

Author

Zak Seidov, Apr 21 2009

Status

approved