A050289
Zeroless pandigital numbers: numbers containing the digits 1-9 (each appearing at least once) and no 0's.
Original entry on oeis.org
123456789, 123456798, 123456879, 123456897, 123456978, 123456987, 123457689, 123457698, 123457869, 123457896, 123457968, 123457986, 123458679, 123458697, 123458769, 123458796, 123458967, 123458976, 123459678, 123459687, 123459768, 123459786, 123459867, 123459876, 123465789
Offset: 1
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apply( {A050289(n)=if(n<=7!*81, fromdigits(Vec(numtoperm(9,n-1)))+(n-1)\9!*10^9, "not yet implemented")}, [1..25]) \\ M. F. Hasler, Jan 07 2020, corrected Aug 11 2022
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from itertools import count, islice, permutations, product
def c(t): return len(set(t)) == 9
def t2i(t): return int("".join(map(str, t)))
def agen():
yield from (t2i(p) for p in permutations(range(1, 10)))
for d in count(10):
yield from (t2i(p) for p in product(range(1, 10), repeat=d) if c(p))
print(list(islice(agen(), 25))) # Michael S. Branicky, May 30 2022, updated Aug 05 2022
A159473
Zeroless pandigital primes with least digit sum (46) starting with the largest and listed in descending order.
Original entry on oeis.org
9876543211, 9876542131, 9876541321, 9876541231, 9876534211, 9876532411, 9876524131, 9876521341, 9876521143, 9876514321, 9876511243, 9876453211, 9876435211, 9876432151, 9876425113, 9876421153, 9876325411, 9876324511
Offset: 1
A159568
Zeroless pandigital emirps.
Original entry on oeis.org
1123564987, 1123586479, 1123869547, 1124356789, 1124378659, 1124685973, 1124698537, 1124753689, 1124763589, 1124785639, 1124879563, 1124895367, 1124896753, 1124956837, 1124978563, 1125347689, 1125386749, 1125398467, 1125487963, 1125648379, 1125748693
Offset: 1
A159569
Pandigital primes that become zeroless pandigital primes when the digit 0 is deleted.
Original entry on oeis.org
10123465789, 10123685749, 10123746859, 10123854679, 10123945687, 10123956487, 10124356789, 10124378569, 10124563987, 10124568793, 10124683759, 10124695783, 10124736859, 10124763589, 10124785639, 10124867539, 10124867593, 10124935687, 10125367849, 10125368749
Offset: 1
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remz(d) = {nd = []; for (i=1, #d, if (d[i] != 0, nd = concat(nd, d[i]))); subst(Pol(nd), x, 10);}
isok(n) = isprime(n) && (d=digits(n)) && (#vecsort(d,,8)==10) && isprime(remz(d));
lista() = forprime(n=10123465789,, if (isok(n), print1(n, ", "))); \\ Michel Marcus, Oct 06 2014
Original entry on oeis.org
10123457689, 20246923478, 30370389375, 40493875054, 50617360823, 60740857680, 70864405549, 80987954228, 91111523175, 101235101824
Offset: 1
The least prime after a(1) is a(59) = 10123457689 + 10123465789 + 10123465897 + 10123485679 + 10123485769 + 10123496857 + 10123547869 + 10123548679 + 10123568947 + 10123578649 + 10123586947 + 10123598467 + 10123654789 + 10123684759 + 10123685749 + 10123694857 + 10123746859 + 10123784569 + 10123846597 + 10123849657 + 10123854679 + 10123876549 + 10123945687 + 10123956487 + 10123965847 + 10123984657 + 10124356789 + 10124358697 + 10124365879 + 10124365987 + 10124369587 + 10124378569 + 10124385967 + 10124389567 + 10124395867 + 10124398657 + 10124536789 + 10124538769 + 10124563789 + 10124563879 + 10124563987 + 10124568793 + 10124576893 + 10124578693 + 10124579863 + 10124583967 + 10124586397 + 10124589637 + 10124593867 + 10124596873 + 10124597683 + 10124635879 + 10124635897 + 10124638759 + 10124659873 + 10124673859 + 10124678953 + 10124683759 + 10124685379 = 597325496783 is prime.
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