A031997 Odd numbers which when cubed give number composed just of the digits 0, 1, 2, 3.

1, 11, 101, 1001, 10001, 100001, 684917, 1000001, 10000001, 100000001, 1000000001, 10000000001, 100000000001, 1000000000001, 10000000000001, 100000000000001, 1000000000000001, 10000000000000001, 100000000000000001, 1000000000000000001

Offset: 1

Author

Robert G. Wilson v, Jun 23 2001

Keywords

• nonn
• base
• more

Comments

Note that 684917 (whose cube is 321302302131323213) so far is the only entry not of the form 10^x + 1.

Crossrefs

Cf. A030175, A043681, A278936, A278937.

Programs

Mathematica

Do[ If[ Union[ IntegerDigits[ n^3 ] ] [ [ -1 ] ] < 4, Print[ n ] ], {n, 1, 10^9, 2} ] (* corrected by Friedjof Tellkamp, Apr 24 2025 *)
(* faster code *)
DigitsLEQ3[n_] := And @@ (LessEqual[#, 3] & /@ IntegerDigits[n])
Arr = {1, 7}; For[i = 1, i < 10, i++, Arr = Flatten[Table[Select[Arr + 10^i j, DigitsLEQ3[Mod[#^3, 10^(i+1)]] &], {j, 0, 9}]]];
Select[Arr, DigitsLEQ3[#^3] &] (* Friedjof Tellkamp, Apr 25 2025 *)

Python

A031997_list = [n for n in range(1,10**6,2) if max(str(n**3)) <= '3'] # Chai Wah Wu, Feb 23 2016

Extensions

Term 0 removed and a(12)-a(17) added by Chai Wah Wu, Feb 25 2016

a(18)-a(20) from Giovanni Resta, Mar 14 2020