cp's OEIS Frontend

A181319 Numbers n with property that there is a different number m such that the lunar squares n*n and m*m are the same.

%I A181319 #20 Aug 06 2014 16:26:29
%S A181319 11011,11012,11013,11014,11015,11016,11017,11018,11019,11021,11022,
%T A181319 11023,11024,11025,11026,11027,11028,11029,11031,11032,11033,11034,
%U A181319 11035,11036,11037,11038,11039,11041,11042,11043,11044,11045,11046,11047,11048,11049,11051,11052,11053,11054,11055,11056,11057,11058
%N A181319 Numbers n with property that there is a different number m such that the lunar squares n*n and m*m are the same.
%H A181319 David Applegate and N. J. A. Sloane, <a href="/A181319/b181319.txt">Table of n, a(n) for n = 1..21894</a>
%H A181319 D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
%e A181319 11011*11011 = 11111*11111 = 111111111, so 11011 and 11111 are members.
%o A181319 (ksh script from David Applegate; assumes the dismal C program dismal2a has been installed)
%o A181319 i=0
%o A181319 while [ $i -lt 100000 ]; do
%o A181319   echo $i $(dismal2a -d mul $i $i)
%o A181319   i=$(($i+1))
%o A181319 done | awk '{
%o A181319   nrt[$2]++;
%o A181319   rt[$2]=rt[$2] " " $1;
%o A181319 }
%o A181319 END{
%o A181319   for (i in rt)
%o A181319     if (nrt[i] > 1)
%o A181319       print i, rt[i];
%o A181319 }' | sort -k1,1n > dismal_multsquares.txt
%Y A181319 Cf. A087019, A180513.
%K A181319 nonn,base
%O A181319 1,1
%A A181319 _David Applegate_ and _N. J. A. Sloane_, Jan 26 2011