A374669 a(n) is the least number with n prime factors (counted with multiplicity) that is the concatenation of two primes.

23, 22, 27, 132, 32, 729, 192, 2112, 1792, 5632, 3072, 59392, 64512, 90112, 110592, 950272, 2260992, 3244032, 786432, 30277632, 7340032, 23068672, 12582912, 494927872, 1333788672, 1375731712, 704643072, 3892314112, 1879048192, 37446746112, 27380416512, 196494753792, 30064771072, 94489280512

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

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.

Maple

cp:= proc(n) local k;
  if n::even then n mod 10 = 2 and isprime((n-2)/10)
  elif n mod 5 = 0 then isprime((n-5)/10)
  else for k from 1 to ilog10(n) do
    if isprime(n mod 10^k) and isprime(floor(n/10^k)) then return true fi
    od;
    false
  fi
end proc:
f:= proc(n) uses priqueue; local pq, p, q, T, TP, j, v;
  initialize(pq);
  insert([-2^n, 2$n], pq);
  do
    T:= extract(pq);
    v:= -T[1];
    if cp(v) then return(v) fi;
    q:= T[-1];
    p:= nextprime(q);
    for j from n+1 to 2 by -1 do
      if T[j] <> q then break fi;
      TP:= [T[1]*(p/q)^(n+2-j), op(T[2..j-1]), p$(n+2-j)];
      insert(TP, pq)
  od od;
end proc:
map(f, [$1..30]);

Crossrefs

Cf. A001222. Second column of A374376.

Sequence in context: A023465 A004464 A255228 * A255221 A072135 A204633

Adjacent sequences: A374666 A374667 A374668 * A374670 A374671 A374672

Keyword

nonn,base

Author

Robert Israel, Jul 15 2024

Status

approved