A046893 a(n) is the least number with exactly n permutations of digits that are primes.

1, 2, 13, 103, 107, 1007, 1036, 1019, 1013, 1049, 1079, 1237, 10099, 10013, 10135, 10123, 10039, 10127, 10079, 10238, 10234, 10235, 10139, 10478, 12349, 12347, 10378, 12359, 14579, 10789, 100336, 10237, 12389, 23579, 10279, 100136, 12379, 10379, 100267, 13789

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base
• look

Comments

From Robert Israel, Feb 07 2023: (Start)

Permutations that have leading zeros are included, in contrast to A046890 where they are not.

If neither A046890(n) nor a(n) have the digit 0, then they are equal. (End)

Links

• Robert Israel, Table of n, a(n) for n = 0..1477

Crossrefs

Cf. A039999, A046890. All terms are in A179239.

Programs

Maple

g:= proc(d) local x,d1,y;
 [seq(seq(seq(x*10^d + y, y = [0,h(x,d1)]),d1=0..d-1),x=1..9)]
end proc:
g(0):= [$0..9]:
h:= proc(x0, d) local y,z; option remember;
      seq(seq(y*10^d+z, z = [procname(y,d-1)]),y=x0..9)
end proc:
for x0 from 1 to 9 do h(x0,0):= $x0 .. 9 od:
f:= proc(n) local t,L,d,P,i;
t:= 0;
L:= convert(n,base,10); d:= nops(L);
for P in combinat:-permute(L) do
  if isprime(add(P[i]*10^(i-1),i=1..d)) then t:= t+1 fi
od;
t
end proc:
N:= 100: # for a(0)..a(N)
V:= Array(0..N): count:= 0:
for d from 0 while count < N+1 do
  for i in g(d) while count < N+1 do
  v:= f(i);
  if v <= N then
    if V[v] = 0 then V[v]:= i; count:= count+1; fi;
  fi
od od:
convert(V,list); # Robert Israel, Feb 07 2023

Mathematica

a = Table[0, {40}]; Do[b = Count[ PrimeQ[ FromDigits /@ Permutations[ IntegerDigits[n]]], True]; If[b < 40 && a[[b + 1]] == 0, a[[b + 1]] = n; Print[b, " ", n]], {n, 1, 110000}]

Python

from sympy import isprime
from sympy.utilities.iterables import multiset_permutations as mp
from itertools import count, islice, combinations_with_replacement as mc
def nd(d): yield from ("".join((f,)+m) for f in "123456789" for m in mc("0123456789", d-1))
def c(s): return sum(1 for p in mp(s) if p[0]!="0" and isprime(int("".join(p))))
def agen(): # generator of sequence terms
    n, adict = 0, dict()
    for digs in count(1):
        for s in nd(digs):
            v = c(s)
            if v not in adict: adict[v] = int(s)
            while n in adict: yield adict[n]; n += 1
print(list(islice(agen(), 40))) # Michael S. Branicky, Feb 08 2023