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A016073
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Undulating squares.
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5
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0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 484, 676, 69696
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Numbers in A033619 that are squares. See A122875 for the square roots.
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KEYWORD
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nonn,fini,full,nice,base
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AUTHOR
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STATUS
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approved
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