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
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon and Eric Angelini, Jul 07 2023
STATUS
approved