A245096 - OEIS

%I #23 Apr 02 2018 15:47:02

%S 4,9,10,20,30,35,46,54,96,100,200,300,325,395,411,520,800,1000,1470,

%T 2000,2448,2700,3000,3144,4000,4209,4633,6400,6947,9000,9051,10000,

%U 12500,13719,20000,21600,25300,30000,34300,35000,46000,51200,54000,61632,72900,96000

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

%C A249853 gives the numbers whose cubes become squares if one of their digits is deleted.

%C Numbers with single-digit squares are not included. - _Davin Park_, Dec 30 2016

%H Paolo P. Lava, <a href="/A245096/b245096.txt">Table of n, a(n) for n = 1..100</a>

%e 4^2 = 16 and (1)^1/3 = 1.

%e 9^2 = 81 and (8)^1/3 = 2 or (1)^1/3 = 1.

%e 10^2 = 100 and (00)^1/3 = 0.

%e 3144^2 = 9884736 and (884736)^1/3 = 96.

%p with(numtheory): P:=proc(q,h) local a,b,k,n;

%p for n from 4 to q do a:=n^2; for k from 0 to ilog10(a) do

%p b:=trunc(a/10^(k+1))*10^k+(a mod 10^k);

%p if b=trunc(evalf((b)^(1/h)))^h then print(n);

%p break; fi; od; od; end: P(10^9,3);

%t f[n_] := !MissingQ@SelectFirst[Delete[IntegerDigits[n^2], #] & /@ Range[IntegerLength[n^2]], IntegerQ@CubeRoot@FromDigits@# &];

%t Select[Range[4, 1000], f] (* _Davin Park_, Dec 30 2016 *)

%t 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 Cf. A249853.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Nov 12 2014