A371239 - OEIS

%I #10 Mar 16 2024 05:22:22

%S 1,2,5,7,13,14,17,22,23,26,41,43,53,67,70,71,77,79,122,130,131,133,

%T 134,149,151,157,158,161,202,203,205,206,211,214,215,229,230,233,238,

%U 239,241,365,367,373,374,377,391,394,395,401,403,445,446,449,454,455,457

%N Squarefree numbers that are zeroless in base 3 (A032924).

%C The relative asymptotic density of this sequence within the zeroless numbers in base 3 is 27/(4*Pi^2) = 1/A214549 = 0.683917... (Banks and Shparlinski, 2004).

%H Amiram Eldar, <a href="/A371239/b371239.txt">Table of n, a(n) for n = 1..10000</a>

%H William D. Banks and Igor E. Shparlinski, <a href="http://dx.doi.org/10.4064/aa112-4-1">Arithmetic properties of numbers with restricted digits</a>, Acta Arithmetica, Vol. 112, No. 4 (2004), pp. 313-332; <a href="https://eudml.org/doc/278042">alternative link</a>.

%t Select[Range[500], !MemberQ[IntegerDigits[#, 3], 0] && SquareFreeQ[#] &]

%o (PARI) is(n) = vecmin(digits(n, 3)) > 0 && issquarefree(n);

%Y Intersection of A005117 and A032924.

%Y Cf. A214549, A371240, A371241.

%K nonn,base,easy

%O 1,2

%A _Amiram Eldar_, Mar 16 2024