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