OFFSET
1,1
COMMENTS
See A367360 for further information.
Let the comma sequence A121805 be known as S or C0.
A366487, the first differences of A121805, is the same as the comma transform of A121805; call it C1.
This sequence is C2 = C(C(S)), the comma transform C iterated twice.
C4 = C2, C5 = C2, ... once the first term (and the last term if the sequence is finite) are removed from the lower iterates of C.
Theorem: C^{i+2}(S) = C^i(S) for i>=2 in general and for i>=0 when all terms of S have two digits and no least significant digit is zero. See link for proof.
Remark. The lexicographically earliest sequence S with C(S) = S is A010850, all 11's.
The sequence contains 2137451 terms, with a(2137451) = 96. The next term does not exist.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..20000
Michael S. Branicky, Comma Comma Proof
PROG
(Python)
from itertools import islice, pairwise
def S(): # generator of comma sequence
an = 1
while True:
yield an
an += 10*(an%10)
children = [an+y for y in range(1, 10) if str(an+y)[0] == str(y)]
if not children: break
an = children[0]
def C(g): # generator of comma transform of sequence passed as a generator
yield from (10*(t%10) + int(str(u)[0]) for t, u in pairwise(g))
def agen(): return C(C(S()))
print(list(islice(agen(), 70))) # Michael S. Branicky, Jan 05 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michael S. Branicky, Jan 05 2024
STATUS
approved