cp's OEIS Frontend

A050288 Pandigital primes.

%I A050288 #32 Feb 16 2025 08:32:40
%S A050288 10123457689,10123465789,10123465897,10123485679,10123485769,
%T A050288 10123496857,10123547869,10123548679,10123568947,10123578649,
%U A050288 10123586947,10123598467,10123654789,10123684759,10123685749,10123694857,10123746859,10123784569,10123846597,10123849657,10123854679
%N A050288 Pandigital primes.
%C A050288 Digits may appear multiple times; density n/log n (almost all primes are pandigital).
%C A050288 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
%H A050288 Charles R Greathouse IV, <a href="/A050288/b050288.txt">Table of n, a(n) for n = 1..10000</a>.
%H A050288 Eric Weisstein's World of Mathematics, "<a href="https://mathworld.wolfram.com/PandigitalNumber.html">Pandigital Number</a>".
%F A050288 a(n) ~ n log n. - _Charles R Greathouse IV_, Sep 14 2012
%F A050288 Intersection of A171102 and A000040. - _Charles R Greathouse IV_, May 04 2013
%t A050288 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_ *)
%o A050288 (PARI) is(n)=isprime(n) && #vecsort(digits(n),,8)>9 \\ _Charles R Greathouse IV_, May 04 2013
%o A050288 (Python)
%o A050288 from sympy import isprime
%o A050288 from itertools import count, islice, product
%o A050288 def agen(): # generator of terms
%o A050288     for d in count(11):
%o A050288         for f in "123456789":
%o A050288             for m in product("0123456789", repeat=d-2):
%o A050288                 for e in "1379":
%o A050288                     t = f + "".join(m) + e
%o A050288                     if len(set(t)) == 10 and isprime(it:=int(t)):
%o A050288                         yield it
%o A050288 print(list(islice(agen(), 20))) # _Michael S. Branicky_, Apr 09 2024
%Y A050288 Cf. A050278.
%K A050288 nonn,base
%O A050288 1,1
%A A050288 _Eric W. Weisstein_