A249853 Numbers whose cubes become squares if one of their digits is deleted.
4, 5, 6, 10, 20, 21, 25, 40, 44, 64, 90, 100, 129, 160, 200, 250, 360, 400, 490, 500, 600, 640, 810, 1000, 1210, 1440, 1690, 1960, 2000, 2025, 2100, 2250, 2500, 2560, 2890, 3240, 3610, 4000, 4400, 4410, 4840, 5025, 5290, 5760, 6250, 6400, 6760, 7290, 7840, 8410
Offset: 1
Examples
21^3 = 9261 and sqrt(961) = 31. 44^3 = 85184 and sqrt(5184) = 72. 45625^3 = 94974853515625 and sqrt(9474853515625) = 3078125.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 100 terms from Paolo P. Lava)
Programs
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Maple
with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do a:=n^3; for k from 1 to ilog10(a) do if type(sqrt(trunc(a/10^(k+1))*10^k+(a mod 10^k)),integer) then print(n); break; fi; od; od; end: P(10^9);
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Mathematica
f[n_] := !MissingQ@SelectFirst[Delete[IntegerDigits[n^3], #] & /@ Range[IntegerLength[n^3]], IntegerQ@Sqrt@FromDigits@# &]; Select[Range[4, 1000], f] (* Davin Park, Dec 30 2016 *)
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