A364040 a(n) is the least positive number with distinct decimal digits and n prime factors, counted with multiplicity, or -1 if there is no such number.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 98304, 327680, 917504, 786432, 1048576, 3145728, 15728640, 31457280, 2845310976, 6398410752, -1, -1, -1, 536870912

Offset

0,2

Comments

a(n) = -1 for n > 29.

Links

Table of n, a(n) for n=0..29.

Example

a(5) = 32 = 2^5 has distinct decimal digits and 5 prime factors counted with multiplicity.

Maple

V:= Array(0..29, -1): count:= 0:
for m from 1 to 10 do
  for L in combinat:-permute([$0..9], m) while count < 27 do
    if L[1] = 0 then next fi;
    x:= add(L[i]*10^(m-i), i=1..m);
    v:= numtheory:-bigomega(x);
    if V[v] = -1 then V[v]:= x; count:= count+1 fi;
  od;
od:
convert(V, list);

Prog

(Python)
from sympy import primeomega
from itertools import count, islice, permutations as P
def agen(): # generator of terms
    adict, n = dict(), 0
    D = [p for d in range(1, 11) for p in P("0123456789", d) if p[0] != "0"]
    for k in (int("".join(t)) for t in D):
        v = primeomega(k)
        if v not in adict:
            adict[v] = k
            while n in adict: yield adict[n]; n += 1
    yield from (adict[n] if n in adict else -1 for n in count(n))
print(list(islice(agen(), 22))) # Michael S. Branicky, Apr 05 2024

Crossrefs

Cf. A363963.

Sequence in context: A274867 A274866 A274865 * A050732 A371863 A260814

Adjacent sequences: A364037 A364038 A364039 * A364041 A364042 A364043

Keyword

sign,base

Author

Zak Seidov and Robert Israel, Jul 02 2023

Status

approved