A243843 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.

6, 38, 34, 15, 265, 161, 1126, 4891, 1253, 250231, 100462, 49869178, 234139657, 68279314, 2318271253, 636542506

Offset

1,1

Comments

a(17) > 10^10, if it exists. - Lucas A. Brown, Oct 09 2022

Links

Table of n, a(n) for n=1..16.

Lucas A. Brown, A243843.py

Carlos Rivera, Puzzle 640. A sequence of semiprimes, The Prime Puzzles and Problems Connection.

Example

The factors of 265 are 5 and 53.
The factors of 553 are 7 and 79.
The factors of 779 are 19 and 41.
The factors of 1941 are 3 and 647.
The factors of 3647 are 7 and 521.
The factors of 7521 are 3, 23, and 109.
265 is the smallest squarefree semiprime that initiates a sequence of this length, so a(5) = 265.

Prog

(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

Crossrefs

Cf. A006881.

Sequence in context: A083373 A320988 A015492 * A039293 A055713 A216384

Adjacent sequences: A243840 A243841 A243842 * A243844 A243845 A243846

Keyword

nonn,base,hard,more

Author

Arkadiusz Wesolowski, Jun 13 2014

Extensions

Definition corrected and terms a(15) and a(16) from Lucas A. Brown, Oct 09 2022

Status

approved