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A368782
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Comma transform of A366487.
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1
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12, 35, 94, 15, 16, 28, 31, 34, 37, 41, 45, 55, 55, 55, 55, 61, 67, 74, 71, 89, 98, 97, 18, 19, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 11, 11, 12, 13, 14, 15, 16, 17, 18, 22, 22, 24, 26, 28, 22, 22, 24, 26, 28, 22, 22, 24, 26, 28, 22, 22, 24, 26, 28, 22, 22
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OFFSET
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1,1
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COMMENTS
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See A367360 for further information.
Let the comma sequence A121805 be known as S or C0.
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.
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LINKS
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PROG
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(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()))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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