login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers k such that the concatenation of numbers from 1 to k is the product of 3 primes (not necessarily distinct).
2

%I #28 Oct 01 2023 07:35:32

%S 2,5,10,13,14,15,31,51,61,67,73

%N Numbers k such that the concatenation of numbers from 1 to k is the product of 3 primes (not necessarily distinct).

%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 M. Fleuren, <a href="http://www.gallup.unm.edu/~smarandache/michafleuren.htm">Factors and primes of Smarandache sequences</a>.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Puzzle 8. Primes by Listing</a>, The Prime Puzzles & Problems Connection.

%F A046460(a(n)) = 3.

%p q:= n-> is(numtheory[bigomega](parse(cat($1..n)))=3):

%p select(q, [$1..35])[]; # _Alois P. Heinz_, Apr 10 2021

%t Select[Range[100],

%t PrimeOmega@FromDigits@Flatten@IntegerDigits@Range@# == 3 &] (* _Robert Price_, Oct 11 2019 *)

%Y Cf. A001222, A046460.

%K nonn,hard,base

%O 1,1

%A _Patrick De Geest_, Aug 15 1998

%E a(10)-a(11) from _Sean A. Irvine_, Apr 10 2021