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A255398
Numbers k such that k^2 lacks the digit 1 in its decimal expansion.
4
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
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
KEYWORD
nonn,base
AUTHOR
Vincenzo Librandi, Feb 22 2015
STATUS
approved