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A050288
Pandigital primes.
31
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
KEYWORD
nonn,base
STATUS
approved