A048342 Numbers k such that the concatenation of the numbers 1, 2, ..., k is squarefree.

1, 3, 4, 5, 7, 10, 11, 13, 14, 15, 19, 21, 22, 23, 29, 30, 31, 33, 34, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 55, 57, 58, 59, 61, 65, 66, 67, 69, 70, 73, 74, 77, 78, 79, 82, 83, 86, 87, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 109, 110, 111, 113, 114, 115

Offset: 1

Author

Patrick De Geest, Feb 15 1999

Keywords

• nonn
• hard
• base

Comments

Contains no multiples of 4 except 4, no terms == 0 or 8 (mod 9), and no multiples of 25. - Robert Israel, Oct 29 2024

Links

• Patrick De Geest, Normal Smarandache Concatenated Numbers, Prime factors from 1 up to n
• Eric Weisstein's World of Mathematics, Consecutive Number Sequences

Crossrefs

Cf. A007908.

Programs

Maple

filter:= n -> numtheory:-issqrfree(parse(cat($1..n))):
select(filter, [$1..50]); # Robert Israel, Oct 29 2024

Mathematica

Select[Range[50],SquareFreeQ[FromDigits[Flatten[IntegerDigits/@Range[#]]]]&] (* The program generates the first 28 terms of the sequence. *) (* Harvey P. Dale, Nov 29 2024 *)

Extensions

More terms from Sean A. Irvine, Jun 13 2021

Name edited by Robert Israel, Oct 29 2024