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A003144
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A self-generating sequence.
(Formerly M2399)
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4
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1, 3, 5, 7, 8, 10, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 32, 34, 36, 38, 40, 42, 44, 45, 47, 49, 51, 52, 54, 56, 58, 60, 62, 64, 65, 67, 69, 71, 73, 75, 76, 78, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 101, 102, 104, 106, 108, 110, 112, 113, 115, 117, 119, 121, 123, 125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 a(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 a 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..10609
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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) = `a` then t1:=[op(t1), i]; fi; od: t1; (N. J. A. Sloane, Nov 01, 2006)
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CROSSREFS
| Cf. A003145, A003146, A080843, A092782.
Sequence in context: A037086 A059565 A187841 * A191251 A191230 A191202
Adjacent sequences: A003141 A003142 A003143 * A003145 A003146 A003147
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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
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