A260263 -id:A260263 - cp's OEIS frontend

A260264 a(n+1) = a(n) + largest digit not in a(n), starting with a(0) = 0.

0, 9, 17, 26, 35, 44, 53, 62, 71, 80, 89, 96, 104, 113, 122, 131, 140, 149, 157, 166, 175, 184, 193, 201, 210, 219, 227, 236, 245, 254, 263, 272, 281, 290, 298, 305, 314, 323, 332, 341, 350, 359, 367, 376, 385, 394, 402, 411, 420, 429, 437, 446, 455, 464, 473, 482

Offset: 0

Eric Angelini and M. F. Hasler, Jul 21 2015

From a(16173532) = 123456798 on, the sequence becomes constant.
From a(324) = 2798 + 6 = 2804 on, this sequence becomes equal to sequence A260263, which has the same definition except for starting with a(1) = 1.
a(10^k) = 9, 89, 874, 8598, 84284, 823330, 8010205, 77737463, 123456798, ...

M. F. Hasler, Table of n, a(n) for n = 0..1000
E. Angelini, Add the biggest absent digit, SeqFan list, Jul 21, 2015

Cf. A045844.

NestList[#+Max[Complement[Range[0,9],IntegerDigits[#]]]&,0,60] (* Harvey P. Dale, May 17 2019 *)

{L=0;a=0;d=vector(9,d,d);for(n=0,1000,n>=L&&print1(a",")+L*=10;a+=vecmax(setminus(d,Set(digits(a)))))} \\ Set L=1 to list only a(10^k).

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.

Original entry on oeis.org

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

Offset: 2

Hans Havermann, Jul 23 2015

			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)

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

Cf. A260263, A260264.

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}]

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

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

cp's OEIS Frontend

A260264 a(n+1) = a(n) + largest digit not in a(n), starting with a(0) = 0.

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