A374669 - OEIS

%I #8 Jul 19 2024 19:15:05

%S 23,22,27,132,32,729,192,2112,1792,5632,3072,59392,64512,90112,110592,

%T 950272,2260992,3244032,786432,30277632,7340032,23068672,12582912,

%U 494927872,1333788672,1375731712,704643072,3892314112,1879048192,37446746112,27380416512,196494753792,30064771072,94489280512

%N a(n) is the least number with n prime factors (counted with multiplicity) that is the concatenation of two primes.

%H Robert Israel, <a href="/A374669/b374669.txt">Table of n, a(n) for n = 1..1000</a>

%e a(4) = 132 because 132 = 2^2 * 3 * 11 is the product of 4 primes (counted with multiplicity) and is the concatenation of the two primes 13 and 2.

%p cp:= proc(n) local k;

%p   if n::even then n mod 10 = 2 and isprime((n-2)/10)

%p   elif n mod 5 = 0 then isprime((n-5)/10)

%p   else for k from 1 to ilog10(n) do

%p     if isprime(n mod 10^k) and isprime(floor(n/10^k)) then return true fi

%p     od;

%p     false

%p   fi

%p end proc:

%p f:= proc(n) uses priqueue; local pq, p, q, T, TP, j, v;

%p   initialize(pq);

%p   insert([-2^n,2$n],pq);

%p   do

%p     T:= extract(pq);

%p     v:= -T[1];

%p     if cp(v) then return(v) fi;

%p     q:= T[-1];

%p     p:= nextprime(q);

%p     for j from n+1 to 2 by -1 do

%p       if T[j] <> q then break fi;

%p       TP:= [T[1]*(p/q)^(n+2-j), op(T[2..j-1]), p$(n+2-j)];

%p       insert(TP, pq)

%p   od od;

%p end proc:

%p map(f, [$1..30]);

%Y Cf.  A001222. Second column of A374376.

%K nonn,base

%O 1,1

%A _Robert Israel_, Jul 15 2024