A016073 Undulating squares.

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

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

Table of n, a(n) for n=0..13.

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

Robert G. Wilson v

Status

approved