A327225 For any n >= 0, let u and v be such that 2 <= u < v and the digits of n in bases u and v are the same up to a permutation and v is minimized; a(n) = u.

2, 2, 3, 4, 5, 6, 7, 3, 9, 4, 11, 5, 13, 4, 15, 7, 5, 5, 19, 6, 21, 5, 3, 7, 25, 6, 6, 13, 4, 9, 7, 7, 33, 8, 8, 11, 7, 7, 7, 19, 13, 13, 10, 10, 7, 7, 5, 9, 49, 9, 8, 5, 4, 10, 13, 13, 9, 9, 9, 19, 61, 10, 10, 10, 9, 9, 5, 9, 6, 13, 11, 11, 73, 10, 9, 12, 9

Offset: 0

Author

Rémy Sigrist, Aug 27 2019

Keywords

• nonn
• base

Comments

For any n >= 0, the sequence is well defined as the representation of n in any base b >= max(2, n+1) corresponds to a single digit n.

(n, u = A327225(n), v = A327226(n)) = (n, n+1, n+2) iff n = 1 or n is in A059809. - Bernard Schott, Aug 31 2019

Examples

			For n = 11:
- the representations of 11 in bases b = 2..9 are:
    b  11 in base b
    -  ------------
    2  "1011"
    3  "102"
    4  "23"
    5  "21"
    6  "15"
    7  "14"
    8  "13"
    9  "12"
- the representation in base 9 is the least that shows the same digits, up to order, to some former base, namely the base 5,
- hence a(11) = 5.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

See A327226 for the corresponding v's.

Cf. A004053, A059809.

Programs

PARI

a(n) = { my (s=[]); for (v=2, oo, my (d=vecsort(digits(n,v))); if (setsearch(s,d), forstep (u=v-1, 2, -1, if (vecsort(digits(n,u))==d, return (u))), s=setunion(s,[d]))) }

Formula

a(n) <= max(2, n+1).