1,1

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.

Also, indices of c 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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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, Table of n, a(n) for n = 1..3136

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) = `c` then t1:=[op(t1), i]; fi; od: (N. J. A. Sloane, Nov 01 2006)

Cf. A003145, A003144, A080843, A092782.

Sequence in context: A107988 A038241 A160907 this_sequence A063237 A026381 A063556

Adjacent sequences: A003143 A003144 A003145 this_sequence A003147 A003148 A003149

nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Apr 16 2004