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

1,2

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

Table of n, a(n) for n=1..64.

Patrick De Geest, Normal Smarandache Concatenated Numbers, Prime factors from 1 up to n

Eric Weisstein's World of Mathematics, Consecutive Number Sequences

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 *)

Crossrefs

Cf. A007908.

Sequence in context: A072556 A047365 A353448 * A159560 A288427 A030502

Adjacent sequences: A048339 A048340 A048341 * A048343 A048344 A048345

Keyword

nonn,hard,base,changed

Author

Patrick De Geest, Feb 15 1999

Extensions

More terms from Sean A. Irvine, Jun 13 2021

Name edited by Robert Israel, Oct 29 2024

Status

approved