OFFSET
1,3
COMMENTS
S is the lexicographycally earliest nontrivial sequence of nonnegative integers with this property (if we try for a(3) the integers 1, 10 or 11, we respectively get these trivial sequences):
S = 1, 1, 1, 1, 1, 1, 1, ...
S = 1, 10, 0, 0, 0, 0, 0, ...
S = 1, 11, 1, 1, 1, 1, 1, ...
LINKS
Eric Angelini and Jean-Marc Falcoz, Boomerang sequences, Personal blog, Feb 1st 2024.
EXAMPLE
a(1) = 0, which multiplied by 0 gives 0
a(2) = 1, which multiplied by 1 gives 1
a(3) = 12
1st digit is 1, which multiplied by 12 gives 12
2nd digit is 2, which multiplied by 12 gives 24
a(4) = 24
1st digit is 2, which multiplied by 24 gives 48
2nd digit is 4, which multiplied by 24 gives 96
a(5) = 48
1st digit is 4, which multiplied by 48 gives 192
2nd digit is 8, which multiplied by 48 gives 384
a(6) = 96
1st digit is 9, which multiplied by 96 gives 864
2nd digit is 6, which multiplied by 96 gives 576
Etc. We see that the above last column reproduces S.
MATHEMATICA
Join[{0, 1}, Nest[Flatten[IntegerDigits@#*#]&, {12}, 5]] (* Giorgos Kalogeropoulos, Feb 01 2024 *)
PROG
(Python)
from itertools import islice
from collections import deque
def agen(): # generator of terms
S = deque([24])
yield from [0, 1, 12]
while True:
an = S.popleft()
yield an
S.extend(an*d for d in map(int, str(an)))
print(list(islice(agen(), 54))) # Michael S. Branicky, Feb 01 2024
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Feb 01 2024
STATUS
approved