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.

A180489 Smallest pandigital number (A171102) divisible by the n-th prime A000040(n).

Original entry on oeis.org

1023456798, 1023456789, 1023467895, 1023456798, 1024375869, 1023456798, 1023457698, 1023458769, 1023475689, 1023468957, 1023458769, 1023654987, 1023458769, 1023469875, 1023467958, 1023459786, 1023457896, 1023458976
Offset: 1

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Author

Lekraj Beedassy, Sep 08 2010

Keywords

Comments

Digits may appear more than once in the multiple, resulting in 11-or-more-digit values of a(n). The first entry for which that happens is a(10545), because the smallest multiple of the 10545th prime 111119 that contains all the digits 0-9 is 92373 * 111119 = 10264395387, and all smaller primes have 10-digit pandigital multiples. - David J. Seal, Sep 18 2017

Examples

			a(1) is the smallest pandigital number divisible by prime(1) = 2, which is 1023456798. - _David J. Seal_, Sep 18 2017
		

Crossrefs

Programs

  • Mathematica
    With[{s = Select[FromDigits@ # & /@ Permutations[Range[0, 9], {10}], # > 10^9 &]}, Table[SelectFirst[s, Divisible[#, Prime@ n] &], {n, 18}]] (* Michael De Vlieger, Sep 18 2017, after Robert G. Wilson v at A171102 *)

A217535 Least number having in its decimal representation each digit n times.

Original entry on oeis.org

1023456789, 10012233445566778899, 100011222333444555666777888999, 1000011122223333444455556666777788889999, 10000011112222233333444445555566666777778888899999, 100000011111222222333333444444555555666666777777888888999999
Offset: 1

Views

Author

M. F. Hasler, Oct 05 2012

Keywords

Crossrefs

Programs

  • Maple
    a:= n-> parse(cat(1,0$n,1$(n-1),seq(i$n, i=2..9))):
    seq(a(n), n=1..10);  # Alois P. Heinz, Jun 25 2017
  • PARI
    A217535(n)=sum(d=1,9,10^(n-(d==1))\9*d*10^(n*(9-d)))+10^(10*n-1)

Formula

a(n) ~ 10^(10n-1). See PARI code for an exact formula.

A292471 Primes that do not divide any 10-digit pandigital number (i.e. any value in A050278).

Original entry on oeis.org

111119, 123457, 178889, 199999, 224467, 246913, 325477, 333337, 333367, 333667, 336667, 345679, 359147, 361909, 387403, 394549, 411113, 419753, 443221, 444449, 449161, 470551, 473219, 476647, 476659, 504323, 506173, 509053, 512683, 513269, 514289, 514357
Offset: 1

Views

Author

David J. Seal, Sep 21 2017

Keywords

Comments

This is the complement in A000040 of the finite list of primes that divide one or more 10-digit pandigital numbers. That finite list has been obtained by computer; it contains 1102173 primes, with the first prime that is not in the list being prime(10545) = 111119 and the last that is in the list being prime(55537259) = 1097393447.

Examples

			a(1) = 111119 because 111119 is prime and does not divide any of the 10-digit pandigital numbers 1023456789, 1023456798, ..., 9876543210, and all smaller primes do divide at least one of them.
		

Crossrefs

A292703 Values of n such that prime(n) does not divide any 10-digit pandigital number (i.e. any value in A050278).

Original entry on oeis.org

10545, 11602, 16237, 17984, 19978, 21788, 28046, 28666, 28669, 28693, 28928, 29629, 30698, 30896, 32869, 33438, 34699, 35373, 37198, 37300, 37639, 39273, 39477, 39755, 39756, 41859, 42003, 42219, 42490, 42538, 42619, 42624
Offset: 1

Views

Author

David J. Seal, Sep 21 2017

Keywords

Comments

This is the complement of the finite list of n such that prime(n) divides one or more 10-digit pandigital numbers. That finite list has been obtained by computer; it contains 1102173 numbers, with the first number that is not in the list being 10545 and the last that is in the list being 55537259.
A292471 is the corresponding list of primes.
These are the values of n for which A180489(n) has more than 10 digits, and also the values of n for which A274328(n) = 0.

Examples

			a(1) = 10545 because prime(10545) = 111119 does not divide any of the 10-digit pandigital numbers 1023456789, 1023456798, ..., 9876543210, and all smaller primes do divide at least one of them.
		

Crossrefs

A302096 a(n) is the smallest pandigital number divisible by n, or 0 if no such pandigital number exists.

Original entry on oeis.org

1023456789, 1023456798, 1023456789, 1023457896, 1023467895, 1023456798, 1023456798, 1023457896, 1023456789, 1234567890, 1024375869, 1023457896, 1023456798, 1023456798, 1023467895, 1023457968, 1023457698, 1023456798, 1023458769, 1234567980, 1023456798, 1024375968
Offset: 1

Views

Author

Rodolfo Kurchan, May 06 2018

Keywords

Comments

Note: in this sequence, "pandigital" numbers are defined as in A050278 (i.e., with each of the ten digits 0..9 appearing exactly once).
The first 99 terms coincide with those of A061604. - Giovanni Resta, May 15 2018
From Jon E. Schoenfield, May 19 2018: (Start)
Record high values exceeding 2*10^9 begin a(10001) = 2650134987, a(20002) = 2750134986, a(27775) = 3012948675, a(40004) = 3760215984, a(44440) = 4123987560, a(50005) = 6820431975, ...
a(n)=0 for every n divisible by 100. Other than multiples of 100, the smallest values of n for which a(n)=0 are 37037 and 55550. The last nonzero term is a(9876543210) = 9876543210. (End)
There are 44021407 nonzero terms. - Michael S. Branicky, Mar 05 2025

Examples

			a(11) = 1024375869 = 11 * 93125079 because it is the smallest pandigital number that is divisible by 11;
a(100) = 0 because there is no pandigital number that is divisible by 100.
		

Crossrefs

Programs

  • Mathematica
    s = Select[FromDigits /@ Permutations[Range[0, 9]], # > 10^9 &]; Table[ SelectFirst[ s, Mod[#, n] == 0 &, 0], {n, 22}] (* Giovanni Resta, May 15 2018 *)
  • Python
    # see link for another program
    from itertools import permutations
    def a(n): return next((t for p in permutations("0123456789") if p[0] != "0" and (t:=int("".join(p)))%n == 0), 0)
    print([a(n) for n in range(1, 23)]) # Michael S. Branicky, Mar 05 2025
Showing 1-5 of 5 results.