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

%I A255398 #29 May 20 2023 03:25:22
%S A255398 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,
%T A255398 53,55,57,58,60,62,63,64,65,66,67,68,70,73,74,75,76,77,78,80,82,83,84,
%U A255398 85,86,87,88,92,93,94,95,97,98,143,144,150,153,155,156,157,158
%N A255398 Numbers k such that k^2 lacks the digit 1 in its decimal expansion.
%H A255398 Mohammed Yaseen, <a href="/A255398/b255398.txt">Table of n, a(n) for n = 1..10000</a>
%F A255398 From _Mohammed Yaseen_, Apr 18 2023: (Start)
%F A255398 The smallest n-digit term ~ sqrt(2) * 10^(n-1).
%F A255398 The largest n-digit term = 10^n - 2 (see A099150). (End)
%e A255398 98 is in this sequence because 98^2 = 9604.
%e A255398 99 is not in this sequence because 99^2 = 9801.
%p A255398 filter:= n -> not member(1, convert(n^2,base,10)):
%p A255398 select(filter, [$0..200]); # _Robert Israel_, Apr 27 2023
%t A255398 Select[Range[0, 200], DigitCount[#^2, 10, 1]==0 &]
%o A255398 (Magma) [n: n in [0..200] | not 1 in Intseq(n^2)];
%o A255398 (Python)
%o A255398 def ok(k): return "1" not in str(k**2)
%o A255398 print([k for k in range(160) if ok(k)]) # _Michael S. Branicky_, Apr 27 2023
%o A255398 (PARI) isok(k) = !vecsearch(Set(digits(k^2)), 1); \\ _Michel Marcus_, Apr 29 2023
%Y A255398 Cf. A052383, A052040, A099150.
%K A255398 nonn,base
%O A255398 1,2
%A A255398 _Vincenzo Librandi_, Feb 22 2015