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 A016073 Undulating squares. 5
 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 484, 676, 69696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Numbers with decimal expansion ababab... which are squares. "Most mathematicians believe we will never find a larger one" - this has now been proved by David Moews. REFERENCES C. A. Pickover, "Keys to Infinity", Wiley 1995, pp. 159, 160. C. A. Pickover, "Wonders of Numbers", Oxford New York 2001, Chapter 52, pp. 123-124, 316-317. Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 68. LINKS D. Moews, Home Page [See the paper "No More Undulating Squares", available in LaTeX, DVI and Postscript] C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review Eric Weisstein's World of Mathematics, Undulating Number. MAPLE 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 MATHEMATICA 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 *) CROSSREFS Numbers in A033619 that are squares. See A122875 for the square roots. Sequence in context: A018884 A050749 A096599 * A115743 A014186 A052062 Adjacent sequences:  A016070 A016071 A016072 * A016074 A016075 A016076 KEYWORD nonn,fini,full,nice,base AUTHOR STATUS approved

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