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A046461 Numbers k such that concatenation of numbers from 1 to k is a semiprime.

%I A046461 #49 Oct 07 2023 21:39:09
%S A046461 3,4,7,34,97
%N A046461 Numbers k such that concatenation of numbers from 1 to k is a semiprime.
%C A046461 From _Sean A. Irvine_, Apr 15 2010, updated Oct 08 2015: (Start)
%C A046461 5053 and 9706 are definite terms of the sequence.
%C A046461 The next potential term is 1651.
%C A046461 A007908(1651) is composite, but has no known prime factor, and its least prime factor likely has at least 45 digits. (End)
%C A046461 If k is a multiple of 10, then k is not a term. - _Chai Wah Wu_, Jan 22 2020
%C A046461 From _Jon E. Schoenfield_, Oct 07 2023: (Start)
%C A046461 k cannot be a term if any of the following are true:
%C A046461    4|k and k > 4  (2*2 would divide the concatenation)
%C A046461    6|k or  6|k-2  (2*3   "     "     "        "      )
%C A046461    9|k or  9|k-8  (3*3   "     "     "        "      )
%C A046461   10|k            (2*5   "     "     "        "      )
%C A046461   15|k or 15|k-5  (3*5   "     "     "        "      )
%C A046461   25|k            (5*5   "     "     "        "      ) (End)
%H A046461 Patrick De Geest, <a href="http://www.worldofnumbers.com/factorlist.htm">Normal Smarandache Concatenated Numbers, Prime factors from 1 up to n</a>.
%H A046461 M. Fleuren, <a href="http://www.gallup.unm.edu/~smarandache/michafleuren.htm">Factors and primes of Smarandache sequences</a>.
%H A046461 M. Fleuren, <a href="http://www.gallup.unm.edu/~smarandache/micha.txt">Smarandache Factors and Reverse factors</a>.
%H A046461 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_008.htm">Puzzle 8. Primes by Listing</a>, The Prime Puzzles and Problems Connection.
%e A046461 A007908(691)=1304238680165623831238651513722972177904593843651*C1916, so A007908(691) is not a semiprime and 691 is not a term of this sequence.
%t A046461 Select[Range[100], Length@FactorInteger@FromDigits@Flatten@IntegerDigits@Range@# == 2 &] (* _Robert Price_, Oct 11 2019 *)
%t A046461 Select[Range[100],PrimeOmega[FromDigits[Flatten[IntegerDigits/@Range[#]]]] == 2&] (* _Harvey P. Dale_, Sep 10 2022 *)
%Y A046461 Cf. A007908, A046460.
%K A046461 nonn,hard,base,more
%O A046461 1,1
%A A046461 _Patrick De Geest_, Aug 15 1998
%E A046461 Simplified definition by _Sean A. Irvine_, Mar 29 2010
%E A046461 a(5) from _Sean A. Irvine_, Mar 29 2010