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Numbers whose cubes become squares if one of their digits is deleted.
4

%I #28 Oct 27 2023 22:15:20

%S 4,5,6,10,20,21,25,40,44,64,90,100,129,160,200,250,360,400,490,500,

%T 600,640,810,1000,1210,1440,1690,1960,2000,2025,2100,2250,2500,2560,

%U 2890,3240,3610,4000,4400,4410,4840,5025,5290,5760,6250,6400,6760,7290,7840,8410

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

%C A245096 gives the numbers whose squares become cubes if one of their digit is deleted.

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

%H Alois P. Heinz, <a href="/A249853/b249853.txt">Table of n, a(n) for n = 1..1000</a> (first 100 terms from Paolo P. Lava)

%e 21^3 = 9261 and sqrt(961) = 31.

%e 44^3 = 85184 and sqrt(5184) = 72.

%e 45625^3 = 94974853515625 and sqrt(9474853515625) = 3078125.

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

%p for n from 1 to q do a:=n^3; for k from 1 to ilog10(a) do

%p if type(sqrt(trunc(a/10^(k+1))*10^k+(a mod 10^k)),integer)

%p then print(n); break; fi; od; od; end: P(10^9);

%t f[n_] := !MissingQ@SelectFirst[Delete[IntegerDigits[n^3], #] & /@ Range[IntegerLength[n^3]], IntegerQ@Sqrt@FromDigits@# &];

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

%Y Cf. A249587, A225885.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Nov 07 2014