A371239 Squarefree numbers that are zeroless in base 3 (A032924).

1, 2, 5, 7, 13, 14, 17, 22, 23, 26, 41, 43, 53, 67, 70, 71, 77, 79, 122, 130, 131, 133, 134, 149, 151, 157, 158, 161, 202, 203, 205, 206, 211, 214, 215, 229, 230, 233, 238, 239, 241, 365, 367, 373, 374, 377, 391, 394, 395, 401, 403, 445, 446, 449, 454, 455, 457

Offset: 1

Author

Amiram Eldar, Mar 16 2024

Keywords

• nonn
• base
• easy

Comments

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).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• William D. Banks and Igor E. Shparlinski, Arithmetic properties of numbers with restricted digits, Acta Arithmetica, Vol. 112, No. 4 (2004), pp. 313-332; alternative link.

Crossrefs

Intersection of A005117 and A032924.

Cf. A214549, A371240, A371241.

Programs

Mathematica

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

PARI

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