A362499 a(n) is the least positive integer that has exactly n anagrams that are semiprimes, or -1 if there is no such integer.

1, 4, 15, 123, 129, 134, 178, 1025, 1148, 1147, 1137, 1145, 1349, 1348, 1357, 10145, 3589, 10258, 10137, 10123, 11269, 10289, 10268, 10247, 10235, 10267, 10234, 10789, 10279, 11378, 10378, 12369, 10349, 10358, 12368, 10357, 12689, 12358, 10459, 12379, 12679, 13489, 12346, 12349, 16789, 12479

Offset

0,2

Comments

a(n) is the least k such that A131371(k) = n.

Leading zeros are not allowed.

Links

Robert Israel, Table of n, a(n) for n = 0..1000

Example

a(3) = 123 because 123 has 3 anagrams that are semiprimes, namely 123 = 3 * 41, 213 = 3 * 71, and 321 = 3 * 107, and no smaller number works.

Maple

g:= proc(s, m) local  t;
  if s[1..m-1] = [0$(m-1)] then op(map(t -> [t, op(s)], [0, $(max(s) ..9)]))
  else op(map(t -> [t, op(s)], [$(max(s) .. 9)]))
  fi
end proc:
f:= proc(L, m) local P, t, i;
  P:= select(t -> t[-1] <> 0 and numtheory:-bigomega(add(t[i]*10^(i-1), i=1..m))=2, combinat:-permute(L));
  nops(P)
end proc:
V:= Array(0..100):
count:= 2: V[0]:= 1: V[1]:= 4:
L:= [seq(seq([b, a], b=[0, $a..9]), a=1..9)]:
for m from 2 while count < 101 do
  for s in L while count < 101 do
    v:= f(s, m);
    if v <= 100 and V[v] = 0 then
      V[v]:= add(s[i]*10^(i-1), i=1..m); count:= count+1;
    fi
  od;
  L:= map(g, L, m)
od:
convert(V, list);

Prog

(Python)
from sympy import factorint
from sympy.utilities.iterables import multiset_permutations as mp
from itertools import count, islice, combinations_with_replacement as mc
def ndgen():
    yield from ((f, )+r for d in count(1) for f in "123456789" for r in mc("0123456789", d-1))
def c(n): # is_semiprime
    return sum(factorint(n).values()) == 2
def f(digs):
    return sum(1 for p in mp(digs) if p[0]!="0" and c(t:=int("".join(p))))
def agen(): # generator of terms
    adict, n = dict(), 0
    for t in ndgen():
        v = f(t)
        if v not in adict: adict[v] = int("".join(t))
        while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 46))) # Michael S. Branicky, Jun 12 2023

Crossrefs

Cf. A131371, A001358.

Sequence in context: A197703 A352608 A136506 * A323564 A246791 A037447

Adjacent sequences: A362496 A362497 A362498 * A362500 A362501 A362502

Keyword

nonn,base,look

Author

Robert Israel, Jun 11 2023

Status

approved