OFFSET
1,3
COMMENTS
Matches the Fibonacci sequence for the first 14 terms. This breaks after the 15th term because the 15th term of the Fibonacci sequence contains a 0.
Empirically, the ratio between consecutive term approach 1. Is this sequence eventually constant?
LINKS
Bryle Morga, Table of n, a(n) for n = 1..10000
Bryle Morga, Log plot of the first 100,000 terms.
FORMULA
a(n+1) = max{a(n), max{A004719(a(i)+a(n)) for 1 <= i < n}}. - Michael S. Branicky, Jul 24 2024
EXAMPLE
a(15) = 521 because:
a(13) + a(14) = 233 + 377 = 610. (contains a 0.)
a(12) + a(14) = 144 + 377 = 521.
PROG
(Python)
from itertools import islice
def z(n): return int(str(n).replace("0", ""))
def agen(): # generator of terms
yield 1
alst = [1, 1]
an = 1
while True:
yield an
an = max(max(z(ai+an) for ai in alst[:-1]), an)
alst.append(an)
print(list(islice(agen(), 45))) # Michael S. Branicky, Jul 24 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bryle Morga, Jul 24 2024
STATUS
approved