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%I #20 Jul 09 2016 00:51:45
%S 0,1,4,9,16,25,36,49,64,81,121,484,676,69696
%N Undulating squares.
%C Numbers with decimal expansion ababab... which are squares.
%C "Most mathematicians believe we will never find a larger one" - this has now been proved by David Moews.
%D C. A. Pickover, "Keys to Infinity", Wiley 1995, pp. 159, 160.
%D C. A. Pickover, "Wonders of Numbers", Oxford New York 2001, Chapter 52, pp. 123-124, 316-317.
%D Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 68.
%H D. Moews, <a href="http://djm.cc/dmoews.html">Home Page</a> [See the paper "No More Undulating Squares", available in LaTeX, DVI and Postscript]
%H C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&format=complete">Zentralblatt review</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UndulatingNumber.html">Undulating Number.</a>
%p select(issqr,[$0..9,seq(seq(seq(a*(10^(d+1)-10^(d+1 mod 2))/99 + b*(10^d - 10^(d mod 2))/99, b=0..9),a=1..9),d=2..6)]); # _Robert Israel_, Jul 08 2016
%t wave[1]=Range[0, 9]; wave[2]=Range[10, 99]; wave[n_] := wave[n] = Select[ Union[ Flatten[{id = IntegerDigits[#]; FromDigits[Prepend[id, id[[2]]]], FromDigits[Append[id, id[[-2]]]]} & /@ wave[n-1]]], 10^(n-1) < # < 10^n &]; A016073 = Reap[Do[Do[wk = wave[n][[k]]; If[IntegerQ[Sqrt[wk]], Sow[wk]], {k, 1, Length[wave[n]]}], {n, 1, 5}]][[2, 1]] (* _Jean-François Alcover_, Dec 28 2012 *)
%Y Numbers in A033619 that are squares. See A122875 for the square roots.
%K nonn,fini,full,nice,base
%O 0,3
%A _Robert G. Wilson v_
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