A243360 -id:A243360 - cp's OEIS frontend

A160402 Primes made up of all distinct digits except 0 and 1.

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

Lekraj Beedassy, May 13 2009

More precisely, "primes made up of all distinct digits from 2 to 9, each occurring once." Since this restricts the number of digits to 8, the sequence is finite.
The last term of this sequence is a(3098) = 98745623. - Nathaniel Johnston, Jun 24 2011
Also numbers n such that the list of divisors of n contains all the digits 1-9 and each digit appears exactly once (in base 10). There are no composite numbers with this property. Numbers n such that A243360(n) = 987654321. - Jaroslav Krizek, Jun 19 2014

Nathaniel Johnston, Table of n, a(n) for n = 1..3098 (full sequence)

Cf. A029743, A106116. Subsequence of A074665.

[n: n in [1..100000000] | Seqint(Sort(&cat[(Intseq(k)): k in Divisors(n)])) eq 987654321] // Jaroslav Krizek, Jun 19 2014

A160402:={}: p:=23456789: while p<=98765432 do d:=convert(p,base,10): ddig:=true: for k from 0 to 9 do if((k<=1 and numboccur(k,d)>0) or (k>=2 and numboccur(k,d)<>1))then ddig:=false:break: fi: od: if(ddig)then A160402:=A160402 union {p}: fi: p:=nextprime(p): od: op(sort(convert(A160402,list))); # Nathaniel Johnston, Jun 24 2011

Keywords "base,fini" added by R. J. Mathar, May 14 2009

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

Jaroslav Krizek, Jun 04 2014

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

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

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

A243361:=func; [A243361(n): n in [1..100]];

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

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; ....

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

A160402 Primes made up of all distinct digits except 0 and 1.

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

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

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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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