A255398 Numbers k such that k^2 lacks the digit 1 in its decimal expansion.

0, 2, 3, 5, 6, 7, 8, 15, 16, 17, 18, 20, 22, 23, 24, 25, 26, 27, 28, 30, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 64, 65, 66, 67, 68, 70, 73, 74, 75, 76, 77, 78, 80, 82, 83, 84, 85, 86, 87, 88, 92, 93, 94, 95, 97, 98, 143, 144, 150, 153, 155, 156, 157, 158

Offset

1,2

Links

Mohammed Yaseen, Table of n, a(n) for n = 1..10000

Formula

From Mohammed Yaseen, Apr 18 2023: (Start)

The smallest n-digit term ~ sqrt(2) * 10^(n-1).

The largest n-digit term = 10^n - 2 (see A099150). (End)

Example

98 is in this sequence because 98^2 = 9604.
99 is not in this sequence because 99^2 = 9801.

Maple

filter:= n -> not member(1, convert(n^2, base, 10)):
select(filter, [$0..200]); # Robert Israel, Apr 27 2023

Mathematica

Select[Range[0, 200], DigitCount[#^2, 10, 1]==0 &]

Prog

(Magma) [n: n in [0..200] | not 1 in Intseq(n^2)];
(Python)
def ok(k): return "1" not in str(k**2)
print([k for k in range(160) if ok(k)]) # Michael S. Branicky, Apr 27 2023
(PARI) isok(k) = !vecsearch(Set(digits(k^2)), 1); \\ Michel Marcus, Apr 29 2023

Crossrefs

Cf. A052383, A052040, A099150.

Sequence in context: A280060 A197433 A153781 * A050025 A255430 A074492

Adjacent sequences: A255395 A255396 A255397 * A255399 A255400 A255401

Keyword

nonn,base

Author

Vincenzo Librandi, Feb 22 2015

Status

approved