A016073 Undulating squares.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 121, 484, 676, 69696

Offset: 0

Author

Robert G. Wilson v

Keywords

• nonn
• fini
• full
• nice
• base

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.

Crossrefs

Numbers in A033619 that are squares. See A122875 for the square roots.

Programs

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 *)