A255357 Natural numbers n, other than multiples of 10, such that n, n^2 and n^3 lack the digit 1 in their decimal expansion.

2, 3, 7, 62, 63, 65, 66, 67, 74, 76, 77, 78, 84, 86, 87, 92, 93, 94, 95, 202, 207, 274, 275, 282, 284, 287, 288, 292, 295, 298, 305, 307, 452, 453, 457, 587, 588, 592, 594, 607, 624, 632, 635, 636, 637, 638, 653, 664, 665, 666, 667, 668, 675, 686, 688, 695, 697, 698, 702, 703, 705, 707

Offset: 1

Author

Zak Seidov, Feb 23 2015

Keywords

• nonn
• base
• look

Examples

			Numbers {2, 3, 7, 62, 63}, their squares {4, 9, 49, 3844, 3969} and cubes {8, 27, 343, 238328, 250047} all are "one-less".
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000027, A052383, A067251, A255398, A255430, A255431.

Programs

Maple

filter:= proc(n) local L,i;
  for i from 1 to 3 do
    L:= convert(n^i,base,10);
    if member(1,L) then return false fi;
  od;
  true
end proc:
select(filter, [seq(seq(10*i+j, j=2..8),i=0..100)]); # Robert Israel, Apr 03 2024

Mathematica

Select[Range[800],NumberDigit[#,0]!=0&&FreeQ[Flatten[ IntegerDigits/@ {#,#^2,#^3}],1]&] (* Harvey P. Dale, Sep 24 2021 *)

Extensions

Definition modified by Harvey P. Dale, Sep 24 2021