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

Author

Jaroslav Krizek, Jun 04 2014

Keywords

• nonn
• base

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; ....