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.

A243360 a(n) = arrange digits of concatenation of divisors of n (A037278, A176558) in decreasing order (in base 10).

Original entry on oeis.org

1, 21, 31, 421, 51, 6321, 71, 8421, 931, 52110, 111, 6432211, 311, 74211, 55311, 864211, 711, 9863211, 911, 54221100, 73211, 222111, 321, 8644322211, 5521, 632211, 97321, 87442211, 921, 65533211100, 311, 86432211, 333111, 743211, 75531, 986643322111, 731
Offset: 1

Views

Author

Jaroslav Krizek, Jun 04 2014

Keywords

Comments

See A243363 = numbers n such that a(n) = 9876543210.

Examples

			For n = 12; divisors of 12: 1, 2, 3, 4, 6, 12; a(12) = 6432211.

Crossrefs

Cf. A037278, A176558, A243361, A243362, A243363, A243364.

Programs

A243361 a(n) = arrange digits of concatenation of divisors of n (A037278, A176558) in increasing order in base 10 (zero digits are omitted).

Original entry on oeis.org

1, 12, 13, 124, 15, 1236, 17, 1248, 139, 1125, 111, 1122346, 113, 11247, 11355, 112468, 117, 1123689, 119, 112245, 11237, 111222, 123, 1122234468, 1255, 112236, 12379, 11224478, 129, 111233556, 113, 11223468, 111333, 112347, 13557, 111223346689, 137
Offset: 1

Views

Author

Jaroslav Krizek, Jun 04 2014

Keywords

Comments

See A243362 = sequence of numbers n such that a(n) = 123456789: 54023, 54203, 500407, 23456789… First prime in this sequence is 23456789.

Examples

			For n = 20; divisors of 20: 1, 2, 4, 5, 10, 20; a(20) = 112245.

Crossrefs

Cf. A037278, A176558, A243360, A243362, A243363, A243364.

Programs

A243362 Numbers n such that A243361(n) = 123456789.

Original entry on oeis.org

54023, 54203, 500407, 23456789, 23458679, 23459687, 23465789, 23465987, 23469587, 23475869, 23478569, 23489657, 23495867, 23496587, 23498567, 23546879, 23546987, 23548697, 23564897, 23564987, 23567849, 23569487, 23576489, 23584679, 23587649, 23589647, 23594687
Offset: 1

Views

Author

Jaroslav Krizek, Jun 04 2014

Keywords

Comments

Supersequence of A243363, A243364 and A160402.
Conjecture 1: sequence is infinite.
Conjecture 2: a(1), a(2) and a(3) are composites; there are no other numbers n > 3 such that a(n) = composite number.

Examples

			Sets of divisors of a(n): (1, 89, 607, 54023); (1, 67, 809, 54203); (1, 83, 6029, 500407); (1, 23456789); …

Crossrefs

Cf. A160402, A243360, A243361, A243363, A243364.

Programs

  • Magma
    [n: n in [1..1000000] | Seqint(Reverse(Sort(&cat[(Intseq(k)): k in Divisors(n)]))) eq 123456789];

Formula

a(1) = 54023; a(2) = 54203; a(3) = 500407; a(4) … a(3101) = A160402; a(3102) ... a(22659) = A243363; ....

A243364 Primes whose reverse concatenation of divisors (A176558) contains all the digits 1-9 exactly once; the number of digits 0 is arbitrary (in base 10).

Original entry on oeis.org

23456789, 23458679, 23459687, 23465789, 23465987, 23469587, 23475869, 23478569, 23489657, 23495867, 23496587, 23498567, 23546879, 23546987, 23548697, 23564897, 23564987, 23567849, 23569487, 23576489, 23584679, 23587649, 23589647, 23594687, 23645879, 23645987
Offset: 1

Views

Author

Jaroslav Krizek, Jun 04 2014

Keywords

Comments

Sequence differs from A160402; a(n) = A160402(n) for first 3098 terms, a(3099) = 203457869.
Subsequence of A243362. Supersequence of A160402 and A243363.
Primes p such that A243361(p) = 123456789.
Conjecture: sequence is infinite.

Examples

			Prime 200000000003456789 is in sequence because A176558(200000000003456789) = 2000000000034567891; each digit 1 - 9 appears exactly once.

Crossrefs

Cf. A160402, A243360, A243361, A243362, A243363.

Formula

a(1) ... a(3098) = A160402; a(3099) ... a(22656) = A243363; ...

A273094 a(n) is the smallest number whose divisors contain each 0..9 digit exactly n times.

Original entry on oeis.org

203457869, 206893558, 507083396, 506815954, 102668478970, 895233580, 26475394180, 887692930, 10708845258, 13306408052, 155503137452, 963213572, 803503960576, 40349550036, 203264657940
Offset: 1

Views

Author

Giovanni Resta, May 15 2016

Keywords

Comments

We also have a(18)=18174907880, a(19)=81418065258, a(20)=257678968520, and a(23)=529539876740. The missing terms are all greater than 10^12.

Examples

			a(1)=203457869, whose divisors are 1 and 203457869 itself. a(2)=206893558, whose divisors, i.e., 1, 2, 103446779, and 206893558, contain each digit 2 times.

Crossrefs

Cf. A038564, A059436, A243363.
Showing 1-5 of 5 results.

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