A255398 - OEIS

%I #29 May 20 2023 03:25:22

%S 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 53,55,57,58,60,62,63,64,65,66,67,68,70,73,74,75,76,77,78,80,82,83,84,

%U 85,86,87,88,92,93,94,95,97,98,143,144,150,153,155,156,157,158

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

%H Mohammed Yaseen, <a href="/A255398/b255398.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Mohammed Yaseen_, Apr 18 2023: (Start)

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

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

%e 98 is in this sequence because 98^2 = 9604.

%e 99 is not in this sequence because 99^2 = 9801.

%p filter:= n -> not member(1, convert(n^2,base,10)):

%p select(filter, [$0..200]); # _Robert Israel_, Apr 27 2023

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

%o (Magma) [n: n in [0..200] | not 1 in Intseq(n^2)];

%o (Python)

%o def ok(k): return "1" not in str(k**2)

%o print([k for k in range(160) if ok(k)]) # _Michael S. Branicky_, Apr 27 2023

%o (PARI) isok(k) = !vecsearch(Set(digits(k^2)), 1); \\ _Michel Marcus_, Apr 29 2023

%Y Cf. A052383, A052040, A099150.

%K nonn,base

%O 1,2

%A _Vincenzo Librandi_, Feb 22 2015