A300062 a(1) = 1, a(n) = the smallest integer > a(n-1) such that Sum_{k=1..n} a(k) written in decimal contains decimal n as a substring.

1, 11, 18, 19, 26, 31, 41, 42, 50, 71, 101, 201, 301, 401, 501, 601, 701, 801, 901, 1001, 1101, 1201, 1301, 1401, 1426, 1476, 1501, 1601, 1701, 1771, 1831, 1901, 2001, 2101, 2201, 2301, 2401, 2501, 2601, 2701, 2801, 2901, 3001, 3101, 3201, 3301, 3324, 3378, 3401

Offset: 1

Author

Chai Wah Wu, Feb 23 2018

Keywords

• nonn
• base

Comments

1 contains 1 as a substring.

1 + 11 = 12 contains 2 as a substring and 11 is the least number > 1 that does that.

1 + 11 + 18 = 30 contains 3 as a substring and 18 is the least number > 11 that does that.

1 + 11 + 18 + 19 = 49 contains 4 as a substring and 19 is the least number > 18 that does that.

In the first 10000 terms the distribution of the least significant digit {0-9} is {201, 8339, 189, 185, 184, 174, 183, 176, 179, 190}. - Robert G. Wilson v, Feb 24 2018

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A162555.

Programs

Mathematica

f[lst_List] := Block[{k = 1 + lst[[-1]], n = ToString[1 + Length@lst], s = Plus @@ lst}, While[StringPosition[ToString[s + k], n] == {}, k++]; Append[lst, k]]; Nest[f, {1}, 50] (* Robert G. Wilson v, Feb 24 2018 *)

Python

A300062_list, s, j = [1], 1, 1
for i in range(2,10001):
    j, si = j + 1, str(i)
    while si not in str(s+j):
        j += 1
    A300062_list.append(j)
    s += j