A243361 -id:A243361 - cp's OEIS frontend

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

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

Jaroslav Krizek, Jun 04 2014

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.

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

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

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

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

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

Jaroslav Krizek, Jun 04 2014

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

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

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

A243360:=func; [A243360(n): n in [1..100]];

A243363 Numbers with divisors containing all the digits 0-9 and each digit appears exactly once (in base 10).

Original entry on oeis.org

203457869, 203465789, 203465897, 203468579, 203475869, 203478659, 203485697, 203485769, 203495867, 203548967, 203564897, 203568947, 203574689, 203584679, 203584769, 203594687, 203596847, 203598467, 203645879, 203645987, 203648957, 203654987, 203659487, 203674589

Offset: 1

Jaroslav Krizek, Jun 04 2014

Primes made up of distinct digits except 1.
There are no composite numbers with divisors containing all the digits 0-9 and each digit appears exactly once.
Subsequence of A029743 (primes with distinct digits).
Numbers n such that A243360(n) = 9876543210.
Sequence contains 19558 terms, the last term is a(19558) = 987625403.

Michael S. Branicky, Table of n, a(n) for n = 1..19558 (full sequence)

Cf. A037278, A176558, A243360, A243361, A243362, A243364.

[n: n in [1..203457879] | Seqint(Sort(&cat[(Intseq(k)): k in Divisors(n)])) eq 9876543210];

Select[Range[203*10^6,204*10^6],Sort[Flatten[IntegerDigits/@ Divisors[#]]] == Range[0,9]&] (* Harvey P. Dale, Aug 22 2016 *)

# generates entire sequence
from sympy import isprime
from itertools import permutations as perms
dist = (int("".join(p)) for p in perms("023456789", 9) if p[0] != "0")
afull = [k for k in dist if isprime(k)]
print(afull[:24]) # Michael S. Branicky, Aug 04 2022

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

Jaroslav Krizek, Jun 04 2014

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.

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

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

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

cp's OEIS Frontend

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

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

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Magma

A243363 Numbers with divisors containing all the digits 0-9 and each digit appears exactly once (in base 10).

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Magma

Mathematica

Python

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).

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