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

1,1

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A299923 A337189 A087358 * A270002 A057736 A181263

Adjacent sequences: A255354 A255355 A255356 * A255358 A255359 A255360

Keyword

nonn,base,look

Author

Zak Seidov, Feb 23 2015

Extensions

Definition modified by Harvey P. Dale, Sep 24 2021

Status

approved