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
Examples
a(4) = 9216 as 9, 2, 1, 6 have alternating parity.
Links
- Sean A. Irvine, Table of n, a(n) for n = 1..53 (terms 1..33 from Giovanni Resta)
Programs
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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 *)
Extensions
a(5) corrected and more terms from Robert Israel, Aug 14 2018
a(18)-a(20) from Giovanni Resta, Aug 16 2018