|
%I #36 Aug 07 2023 11:33:16
%S 6,38,34,15,265,161,1126,4891,1253,250231,100462,49869178,234139657,
%T 68279314,2318271253,636542506
%N a(n) is the smallest squarefree semiprime that belongs to a sequence of length n under repeated iteration of the map (k -> concatenation of prime divisors of k in increasing order) until a number is reached that is not a squarefree semiprime.
%C a(17) > 10^10, if it exists. - _Lucas A. Brown_, Oct 09 2022
%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A243843.py">A243843.py</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_640.htm">Puzzle 640. A sequence of semiprimes</a>, The Prime Puzzles and Problems Connection.
%e The factors of 265 are 5 and 53.
%e The factors of 553 are 7 and 79.
%e The factors of 779 are 19 and 41.
%e The factors of 1941 are 3 and 647.
%e The factors of 3647 are 7 and 521.
%e The factors of 7521 are 3, 23, and 109.
%e 265 is the smallest squarefree semiprime that initiates a sequence of this length, so a(5) = 265.
%o (Magma) lst:=[]; Factors:=func<k | Factorization(k)>; IsSemiprime:=func<k | &+[d[2]: d in Factors(k)] eq 2>; IsOK:=func<k | IsSemiprime(k) and IsSquarefree(k)>; PrimeDivisors:=func<k | &cat[[Factors(k)[j, 1]: i in [1..Factors(k)[j, 2]]]: j in [1..#Factors(k)]]>; ConcatOfPrimeDivisors:=func<k | Seqint(Reverse(&cat[Reverse(IntegerToSequence(PrimeDivisors(k)[i])): i in [1..#PrimeDivisors(k)]]))>; for n in [1..9] do k:=1; repeat k+:=1; t:=0; if IsOK(k) then b:=k; while IsOK(b) do b:=ConcatOfPrimeDivisors(b); t+:=1; end while; end if; until t eq n; Append(~lst, k); end for; lst; // _Arkadiusz Wesolowski_, Aug 07 2023
%Y Cf. A006881.
%K nonn,base,hard,more
%O 1,1
%A _Arkadiusz Wesolowski_, Jun 13 2014
%E Definition corrected and terms a(15) and a(16) from _Lucas A. Brown_, Oct 09 2022
| 