cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Views

Author

Keywords

Comments

The first 9! = 362880 terms of this sequence are permutations of the digits 1-9 with a(9!) = 987654321. - Jeremy Gardiner, May 28 2010
First differences are given in A209280 (for the first 9! terms) or in A219664 (for at least as much initial terms). - M. F. Hasler, Mar 03 2013
A230959(a(n)) = 0. - Reinhard Zumkeller, Nov 02 2013
After the first 9! terms, 8! + 7! = 9*7! of the initial terms are repeated with a leading '1' prefixed, cf. formula. However, a(9!+8!+7!) = 1219...3 is followed by 122...9 and permutations of the last 7 digits, before 12314..9. - M. F. Hasler, Jan 08 2020, corrected Aug 11 2022 thanks to a remark from Michael S. Branicky

Crossrefs

Programs

  • PARI
    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
    
  • Python
    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

Formula

a(n + 9!) = a(n) + 10^9 for 1 <= n <= 8! + 7!. - M. F. Hasler, Jan 08 2020, corrected Aug 11 2022

Extensions

Name clarified by Michael S. Branicky, 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

Views

Author

Lekraj Beedassy, Apr 13 2009

Keywords

Comments

The last term is a(152526) = 1123465789. - Jinyuan Wang, Aug 14 2020

Crossrefs

Cf. A050290.

Extensions

Corrected and extended by Ray Chandler, Apr 16 2009

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

Views

Author

Lekraj Beedassy, Apr 15 2009

Keywords

Comments

There are 56104 10-digit terms. - Jud McCranie, Jul 01 2013

Crossrefs

Extensions

Corrected and more terms added by Jud McCranie, Jul 01 2013

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

Views

Author

Lekraj Beedassy, Apr 15 2009

Keywords

Crossrefs

Programs

  • PARI
    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

Extensions

Missing terms a(2)-a(6) and a(15)-a(20) added by Hiroaki Yamanouchi, Oct 06 2014

A173051 Partial sums of A050288.

Original entry on oeis.org

10123457689, 20246923478, 30370389375, 40493875054, 50617360823, 60740857680, 70864405549, 80987954228, 91111523175, 101235101824
Offset: 1

Views

Author

Jonathan Vos Post, Feb 08 2010

Keywords

Comments

Partial sums of (base 10) Pandigital primes. Note that almost all primes are pandigital. a(59) is (after the first value) the first prime in this sequence. What is the smallest pandigital prime partial sum of (base 10) pandigital primes? In other bases?

Examples

			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.
		

Crossrefs

Formula

a(n) = SUM[i=1..n] A050288(i) = SUM[i=1..n] {p is prime and p, base 10, has all 10 digits in its decimal representation, digits may appear multiple times}.
Showing 1-5 of 5 results.