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Numbers k such that the concatenation of the numbers 1, 2, ..., k is squarefree.
3

%I #28 Nov 29 2024 13:19:42

%S 1,3,4,5,7,10,11,13,14,15,19,21,22,23,29,30,31,33,34,37,38,39,41,42,

%T 43,46,47,49,51,55,57,58,59,61,65,66,67,69,70,73,74,77,78,79,82,83,86,

%U 87,91,93,94,95,97,101,102,103,105,106,109,110,111,113,114,115

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

%C Contains no multiples of 4 except 4, no terms == 0 or 8 (mod 9), and no multiples of 25. - _Robert Israel_, Oct 29 2024

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/factorlist.htm">Normal Smarandache Concatenated Numbers, Prime factors from 1 up to n</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConsecutiveNumberSequences.html">Consecutive Number Sequences</a>

%p filter:= n -> numtheory:-issqrfree(parse(cat($1..n))):

%p select(filter, [$1..50]); # _Robert Israel_, Oct 29 2024

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

%Y Cf. A007908.

%K nonn,hard,base

%O 1,2

%A _Patrick De Geest_, Feb 15 1999

%E More terms from _Sean A. Irvine_, Jun 13 2021

%E Name edited by _Robert Israel_, Oct 29 2024