A123699 Smallest b such that all digits are distinct in base b representation of n.

1, 2, 3, 4, 3, 3, 3, 4, 4, 5, 3, 4, 4, 4, 3, 5, 5, 4, 3, 5, 3, 5, 5, 4, 6, 6, 4, 4, 5, 4, 6, 6, 4, 6, 4, 4, 7, 5, 4, 5, 6, 5, 7, 4, 4, 7, 5, 5, 4, 4, 5, 4, 5, 4, 5, 4, 4, 5, 5, 6, 8, 6, 6, 9, 5, 5, 7, 6, 5, 5, 5, 7, 5, 7, 4, 5, 5, 4, 5, 5, 6, 5, 6, 5, 5, 5, 7, 7, 5, 6, 6, 8, 7, 6, 5, 5, 5, 8, 4, 11, 5, 5, 5, 7, 5

Offset

1,2

Comments

a(A123700(n)) = n and a(m) <> n for m < A123700(n).

See A126688 for another version of the same sequence. - R. J. Mathar, Jun 15 2008

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

n=10: 1010 [b=2] = 101 [b=3] = 22 [b=4] = 20 [b=5]: a(10)=5;
n=11: 1011 [b=2] = 102 [b=3]: a(11)=3;
n=12: 1100 [b=2] = 110 [b=3] = 30 [b=4]: a(12)=4;
n=13: 1101 [b=2] = 111 [b=3] = 31 [b=4]: a(13)=4;
n=14: 1110 [b=2] = 112 [b=3] = 32 [b=4]: a(14)=4;
n=15: 1111 [b=2] = 120 [b=3]: a(15)=3.

Prog

(PARI) a(n) = if (n==1, 1, my(b = 2, do = 1); while (do, vb = digits(n, b); if (#vb == #Set(vb), do = 0, b++); ); b); \\ Michel Marcus, Jun 09 2013; corrected Jun 14 2022
(Python)
from sympy.ntheory.digits import digits
def distinct(n, b): d = digits(n, b); return len(d) == len(set(d))
def a(n):
    if n == 1: return 1
    b = 2
    while not distinct(n, b): b += 1
    return b
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Jun 15 2022

Crossrefs

Cf. A126688, A123700.

Sequence in context: A101497 A274007 A065870 * A322808 A352899 A119352

Adjacent sequences: A123696 A123697 A123698 * A123700 A123701 A123702

Keyword

nonn,base

Author

Reinhard Zumkeller, Oct 08 2006

Status

approved