|
%I #21 Apr 20 2016 01:25:14
%S 0,1,4,9,16,25,36,49,64,81,100,144,196,225,289,324,400,441,484,576,
%T 625,784,841,900,1024,1156,1444,1600,1764,1936,2025,2209,2401,2601,
%U 2809,3136,3364,3600,3844,4225,4489,4624,5184,5776,6084,6241,6400
%N Squares with property that all even digits occur together and all odd digits occur together.
%C Among first 22083 terms (up to 10^14), there are 19202 even and 2881 odd terms. Also note that in odd terms, the only odd digit is the last one. - _Zak Seidov_, Apr 17 2016
%C From _Robert Israel_, Apr 18 2016: (Start)
%C For any k>=1, (10^k-2)^2 is a member of the sequence with the first k-1 digits odd and the last k+1 even, while (2*10^k+2)^2 = 4*10^(2*k)+8*10^k+4 is a member with all digits even, and (2*10^k+1)^2 is an odd member.
%C If x is an even member, then so is 100*x. (End)
%H Zak Seidov, <a href="/A030476/b030476.txt">Table of n, a(n) for n = 0..22082</a>
%e a(21054)=9427771^2=88882866028441, - _Zak Seidov_, Apr 18 2016
%e a(21055)=9427980^2=88886806880400. - _Robert Israel_, Apr 18 2016
%p filter:= proc(n) local L,evens,odds;
%p L:= convert(n,base,10) mod 2;
%p evens:= select(t -> L[t]::even, [$1..nops(L)]);
%p odds:= select(t -> L[t]::odd, [$1..nops(L)]);
%p (evens = []) or (odds = []) or (evens[1]>odds[-1]) or (odds[1]>evens[-1])
%p end proc:
%p select(filter, [seq(i^2,i=0..100)]); # _Robert Israel_, Apr 18 2016
%t Select[Range[0, 80]^2, Function[k, Or[Flatten@ # == k, Flatten@ Reverse@ # == k] &@ GatherBy[k, EvenQ]]@ IntegerDigits@ # &] (* _Michael De Vlieger_, Apr 17 2016 *)
%K nonn,base
%O 0,3
%A _Patrick De Geest_
|
