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

1,2

Comments

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

Links

Table of n, a(n) for n=1..20.

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 *)

Prog

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

Crossrefs

Cf. A030175, A043681, A278936, A278937.

Sequence in context: A171750 A191420 A118937 * A116098 A116129 A000533

Adjacent sequences: A031994 A031995 A031996 * A031998 A031999 A032000

Keyword

nonn,base,more

Author

Robert G. Wilson v, Jun 23 2001

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

Status

approved