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
Examples
98 is in this sequence because 98^2 = 9604. 99 is not in this sequence because 99^2 = 9801.
Links
- Mohammed Yaseen, Table of n, a(n) for n = 1..10000
Programs
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Magma
[n: n in [0..200] | not 1 in Intseq(n^2)];
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Maple
filter:= n -> not member(1, convert(n^2,base,10)): select(filter, [$0..200]); # Robert Israel, Apr 27 2023
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Mathematica
Select[Range[0, 200], DigitCount[#^2, 10, 1]==0 &]
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PARI
isok(k) = !vecsearch(Set(digits(k^2)), 1); \\ Michel Marcus, Apr 29 2023
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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
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)