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A245096
Numbers whose squares become cubes if one of their digits is deleted.
2
4, 9, 10, 20, 30, 35, 46, 54, 96, 100, 200, 300, 325, 395, 411, 520, 800, 1000, 1470, 2000, 2448, 2700, 3000, 3144, 4000, 4209, 4633, 6400, 6947, 9000, 9051, 10000, 12500, 13719, 20000, 21600, 25300, 30000, 34300, 35000, 46000, 51200, 54000, 61632, 72900, 96000
OFFSET
1,1
COMMENTS
A249853 gives the numbers whose cubes become squares if one of their digits is deleted.
Numbers with single-digit squares are not included. - Davin Park, Dec 30 2016
LINKS
EXAMPLE
4^2 = 16 and (1)^1/3 = 1.
9^2 = 81 and (8)^1/3 = 2 or (1)^1/3 = 1.
10^2 = 100 and (00)^1/3 = 0.
3144^2 = 9884736 and (884736)^1/3 = 96.
MAPLE
with(numtheory): P:=proc(q, h) local a, b, k, n;
for n from 4 to q do a:=n^2; for k from 0 to ilog10(a) do
b:=trunc(a/10^(k+1))*10^k+(a mod 10^k);
if b=trunc(evalf((b)^(1/h)))^h then print(n);
break; fi; od; od; end: P(10^9, 3);
MATHEMATICA
f[n_] := !MissingQ@SelectFirst[Delete[IntegerDigits[n^2], #] & /@ Range[IntegerLength[n^2]], IntegerQ@CubeRoot@FromDigits@# &];
Select[Range[4, 1000], f] (* Davin Park, Dec 30 2016 *)
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 *)
CROSSREFS
Cf. A249853.
Sequence in context: A004631 A316113 A336256 * A352097 A354853 A119718
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Nov 12 2014
STATUS
approved