A260351 In base n, a(n) is the largest (decimal equivalent) number reached when one sequentially adds to a sum, starting with zero, the largest digit not in that sum.

1, 5, 30, 214, 1865, 22881, 342447, 6053444, 123456798, 2853116815, 73686782411, 2103299351346, 65751519678065, 2234152501943369, 81985529216487165, 3231407272993503256, 136146740744970718253, 6106233505124424781971, 290464265927977839351196

Offset: 2

Author

Hans Havermann, Jul 23 2015

Keywords

• nonn
• base

Examples

			In base 4:
0 + 3 = 3 (= 3)
3 + 2 = 5 (= 11)
5 + 3 = 8 (= 20)
8 + 3 = 11 (= 23)
11 + 1 = 12 (= 30)
12 + 2 = 14 (= 32)
14 + 1 = 15 (= 33)
15 + 2 = 17 (= 101)
17 + 3 = 20 (= 110)
20 + 3 = 23 (= 113)
23 + 2 = 25 (= 121)
25 + 3 = 28 (= 130)
28 + 2 = 30 (= 132)
30 + 0 = 30 (repeat, therefore a(4) = 30)
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 2..22
• Frank Adams-Watters, Add the biggest absent digit, SeqFan list, July 21, 2015

Crossrefs

Cf. A260263, A260264.

Programs

Mathematica

Table[r=Range[0, b-1]; s=0; t=1; While[t!=0, t=Complement[r, IntegerDigits[s, b]][[-1]]; s=s+t]; s, {b, 2, 8}]

Python

from gmpy2 import digits
def A260351(n):
    r, c = set([digits(d,n) for d in range(n)]), 0
    dc = set(digits(c,n))
    while len(dc) < n-1 or '0' in dc:
        c += max([int(d,n) for d in r - dc])
        dc = set(digits(c,n))
    return c # Chai Wah Wu, Jul 24 2015

Extensions

a(13) from Giovanni Resta, Jul 23 2015

a(14) from Giovanni Resta, Jul 24 2015

a(15)-a(20) from Hiroaki Yamanouchi, Aug 01 2015