A050288 Pandigital primes.

10123457689, 10123465789, 10123465897, 10123485679, 10123485769, 10123496857, 10123547869, 10123548679, 10123568947, 10123578649, 10123586947, 10123598467, 10123654789, 10123684759, 10123685749, 10123694857, 10123746859, 10123784569, 10123846597, 10123849657, 10123854679

Offset

1,1

Comments

Digits may appear multiple times; density n/log n (almost all primes are pandigital).

Note that actually a(n) is much larger than n*log(n) (see Formula section). Even for n = 10000, a(n) = 111571*n*log(n). - Zak Seidov, Jul 27 2014

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000.

Eric Weisstein's World of Mathematics, "Pandigital Number".

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Sep 14 2012

Intersection of A171102 and A000040. - Charles R Greathouse IV, May 04 2013

Mathematica

ta={{0}}; Do[u=Union[IntegerDigits[n]]; If[Equal[u, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}]&&PrimeQ[n], ta=Append[ta, n]], {n, 10123456789, 20000000000}]; ta (* Labos Elemer *)

Prog

(PARI) is(n)=isprime(n) && #vecsort(digits(n), , 8)>9 \\ Charles R Greathouse IV, May 04 2013
(Python)
from sympy import isprime
from itertools import count, islice, product
def agen(): # generator of terms
    for d in count(11):
        for f in "123456789":
            for m in product("0123456789", repeat=d-2):
                for e in "1379":
                    t = f + "".join(m) + e
                    if len(set(t)) == 10 and isprime(it:=int(t)):
                        yield it
print(list(islice(agen(), 20))) # Michael S. Branicky, Apr 09 2024

Crossrefs

Cf. A050278.

Sequence in context: A172688 A112388 A225298 * A173051 A159569 A159292

Adjacent sequences: A050285 A050286 A050287 * A050289 A050290 A050291

Keyword

nonn,base

Author

Eric W. Weisstein

Status

approved