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A276788
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First differences of A003144.
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8
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2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2
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OFFSET
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1,1
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COMMENTS
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In A276790, leave 2's unchanged, but replace 1's by 2's and 0's by 1's, and then omit the initial 1.
If we prefixed A003144 with an initial 0, then its first differences would be a' := 1 followed by a, that is, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, ... If we now add 1 to every term of a' we get A305374 = first differences of A140101. - N. J. A. Sloane, Jul 17 2018
(a(n)) is a morphic sequence: in the tribonacci word A092782 = 1,2,1,3,1,2,1,1,... map 1 -> 2, 2 -> 2, 3 -> 1. - Michel Dekking, Mar 21 2019
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LINKS
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FORMULA
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MAPLE
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M:= 10: # to use M generations of strings
S[1]:="a": S[2]:="ab": S[3]:="abac":
for n from 4 to M do S[n]:=cat(S[n-1], S[n-2], S[n-3]); od:
P:=select(t -> S[M][t]="a", [$1..length(S[M])]):
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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