A068881 Largest n-digit square with property that digits alternate in parity, or 0 if no such number exists.

9, 81, 961, 9216, 96721, 929296, 9690769, 98525476, 987656329, 9618509476, 98987632129, 987650365636, 9890943230169, 98987854141696, 987896383010761, 9896907878105616, 98989096389856929, 989894587654967296, 9898969096969272961, 98985494707696721476

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..53 (terms 1..33 from Giovanni Resta)

Example

a(4) = 9216 as 9, 2, 1, 6 have alternating parity.

Maple

alp:= proc(n) local L, d;
L:= convert(n, base, 10);
d:= nops(L);
if d::even then L:= L + map(op, [[0, 1]$(d/2)]) else L:= L + map(op, [[0, 1]$((d-1)/2), [0]]) fi;
nops(convert(L mod 2, set))=1
end proc:f:= proc(d) local s;
  for s from floor(sqrt(10^d)) by -1 to ceil(sqrt(10^(d-1))) do
    if alp(s^2) then return s^2 fi
  od;
  0
end proc:map(f, [$1..10]); # Robert Israel, Aug 14 2018

Mathematica

altQ[n_] := n < 10 || Union[Total /@ Partition[ Mod[ IntegerDigits@ n, 2], 2, 1]] == {1}; a[n_] := Block[{r = Floor@ Sqrt@ FromDigits[8 + Mod[ Range@ n, 2]]}, While[! altQ[r^2], r--]; r^2]; Array[a, 16] (* Giovanni Resta, Aug 17 2018 *)

Crossrefs

Cf. A068876, A030152, A068880.

Sequence in context: A187122 A113361 A180737 * A104266 A061433 A069659

Adjacent sequences: A068878 A068879 A068880 * A068882 A068883 A068884

Keyword

base,nonn

Author

Amarnath Murthy, Mar 19 2002

Extensions

a(5) corrected and more terms from Robert Israel, Aug 14 2018

a(18)-a(20) from Giovanni Resta, Aug 16 2018

Status

approved