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A245096 Numbers whose squares become cubes if one of their digits is deleted.

%I A245096 #23 Apr 02 2018 15:47:02
%S A245096 4,9,10,20,30,35,46,54,96,100,200,300,325,395,411,520,800,1000,1470,
%T A245096 2000,2448,2700,3000,3144,4000,4209,4633,6400,6947,9000,9051,10000,
%U A245096 12500,13719,20000,21600,25300,30000,34300,35000,46000,51200,54000,61632,72900,96000
%N A245096 Numbers whose squares become cubes if one of their digits is deleted.
%C A245096 A249853 gives the numbers whose cubes become squares if one of their digits is deleted.
%C A245096 Numbers with single-digit squares are not included. - _Davin Park_, Dec 30 2016
%H A245096 Paolo P. Lava, <a href="/A245096/b245096.txt">Table of n, a(n) for n = 1..100</a>
%e A245096 4^2 = 16 and (1)^1/3 = 1.
%e A245096 9^2 = 81 and (8)^1/3 = 2 or (1)^1/3 = 1.
%e A245096 10^2 = 100 and (00)^1/3 = 0.
%e A245096 3144^2 = 9884736 and (884736)^1/3 = 96.
%p A245096 with(numtheory): P:=proc(q,h) local a,b,k,n;
%p A245096 for n from 4 to q do a:=n^2; for k from 0 to ilog10(a) do
%p A245096 b:=trunc(a/10^(k+1))*10^k+(a mod 10^k);
%p A245096 if b=trunc(evalf((b)^(1/h)))^h then print(n);
%p A245096 break; fi; od; od; end: P(10^9,3);
%t A245096 f[n_] := !MissingQ@SelectFirst[Delete[IntegerDigits[n^2], #] & /@ Range[IntegerLength[n^2]], IntegerQ@CubeRoot@FromDigits@# &];
%t A245096 Select[Range[4, 1000], f] (* _Davin Park_, Dec 30 2016 *)
%t A245096 scddQ[x_]:=AnyTrue[Table[FromDigits[Delete[IntegerDigits[x^2],n]],{n, IntegerLength[ x^2]}],IntegerQ[CubeRoot[#]]&]; Select[Range[100000], scddQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 02 2018 *)
%Y A245096 Cf. A249853.
%K A245096 nonn,base
%O A245096 1,1
%A A245096 _Paolo P. Lava_, Nov 12 2014