A363186 Lexicographically earliest sequence of distinct positive integers such that the sum of all terms a(1)..a(n) is a substring of the concatenation of all terms a(1)..a(n).

1, 10, 98, 767, 111, 122, 2, 11, 100, 889, 110, 4490, 400, 560, 1096, 124, 20, 129, 70, 502, 93, 171, 212, 361, 512, 26, 21, 36, 54, 14, 1011, 139, 99, 59, 550, 684, 345, 102, 1021, 1999, 2871, 137, 892, 89, 126, 875, 510, 994, 586, 2012, 662, 1836, 201, 405, 388, 2007, 2798, 1641, 50, 340

Offset

1,2

Comments

In the first 10000 terms the smallest number that has not yet appeared is 696; it is therefore likely all numbers eventually appear although this is unknown.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Eric Angelini, Échecs et Maths, Personal blog, July 2023.

Example

a(2) = 10 as a(1) + 10 = 1 + 10 = 11 which is a substring of "1" + "10" = "110".
a(3) = 98 as a(1) + a(2) + 98 = 1 + 10 + 98 = 109 which is a substring of "1" + "10" + "98" = "11098".
a(4) = 767 as a(1) + a(2) + a(3) + 767 = 1 + 10 + 98 + 767 = 876 which is a substring of "1" + "10" + "98" + "767" = "11098767".

Prog

(Python)
from itertools import islice
def agen(): # generator of terms
    s, mink, aset, concat = 1, 2, {1}, "1"
    yield from [1]
    while True:
        an = mink
        while an in aset or not str(s+an) in concat+str(an): an += 1
        aset.add(an); s += an; concat += str(an); yield an
        while mink in aset: mink += 1
print(list(islice(agen(), 60))) # Michael S. Branicky, Feb 08 2024

Crossrefs

Cf. A359482, A300000, A339144, A357082.

Sequence in context: A308523 A190985 A044642 * A264462 A198968 A125946

Adjacent sequences: A363183 A363184 A363185 * A363187 A363188 A363189

Keyword

nonn,base

Author

Scott R. Shannon and Eric Angelini, Jul 07 2023

Status

approved