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A003145
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A self-generating sequence.
(Formerly M1571)
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4
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2, 6, 9, 13, 15, 19, 22, 26, 30, 33, 37, 39, 43, 46, 50, 53, 57, 59, 63, 66, 70, 74, 77, 81, 83, 87, 90, 94, 96, 100, 103, 107, 111, 114, 118, 120, 124, 127, 131, 134, 138, 140, 144, 147, 151, 155, 158, 162, 164, 168, 171, 175, 179, 182, 186, 188, 192, 195, 199, 202, 206, 208
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Comment from Philippe DELEHAM: A003144, A003145, A003146 may be defined as follows. Consider the maps a -> ab, b ->ac, c ->a, starting from S(1) = a; then A003144 gives the indices of a, A003145 gives the indices of b and A003146 gives the indices of c. The sequence of letters in the infinite word begins a, b, a, c, a, b, a, a, b, a, c, a, b, a, b, a, c, ... Setting a = 1, b = 2, c = 3 gives A092782. Setting a = 0, b = 1, c = 2 gives A080843.
Also indices of b in the sequence closed under a -> abac, b -> aba, c -> ab; starting with a(1) = a. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Apr 16 2004
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REFERENCES
| L. Belanger and S. Brlek, On tribonacci sequences, preprint, 1998.
L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations of higher order, Fib. Quart., 10 (1972), 43-69.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 1..5768
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MAPLE
| M:=17; 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:
t0:=S[M]: l:=length(t0); t1:=[];
for i from 1 to l do if substring(t0, i..i) = `b` then t1:=[op(t1), i]; fi; od: (N. J. A. Sloane)
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CROSSREFS
| Cf. A003144, A003146, A080843, A092782.
Sequence in context: A169915 A086562 A083789 * A184621 A184821 A184869
Adjacent sequences: A003142 A003143 A003144 * A003146 A003147 A003148
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Apr 16 2004
Corrected by T. D. Noe and N. J. A. Sloane (njas(AT)research.att.com), Nov 01 2006
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