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A321021 a(0)=0, a(1)=1; thereafter a(n) = a(n-2)+a(n-1), keeping just the digits that appear exactly once. 3

%I

%S 0,1,1,2,3,5,8,13,21,34,0,34,34,68,102,170,7,1,8,9,17,26,43,69,2,71,

%T 73,1,74,75,149,4,153,157,310,467,0,467,467,934,40,974,4,978,982,1960,

%U 94,2054,2148,40,21,61,82,143,5,148,153,301,5,306,3

%N a(0)=0, a(1)=1; thereafter a(n) = a(n-2)+a(n-1), keeping just the digits that appear exactly once.

%C a(n) = A320486(a(n-2)+a(n-1)).

%C This must eventually enter a cycle, since there are only finitely many pairs of numbers that both have distinct digits. In fact, at step 171, enters a cycle of length 100 (see A321022).

%C Another entry into this cycle would be to start with 2, 1 and use the same rule, in which case the sequence would begin (2, 1, 3, 4, 7, 0, 7, 7, 14, 21, 35, 56, 91, 147, 238, 385, 623, ..., 40, 80, 120), a cycle of length 100 that repeats (cf. A321022).

%H N. J. A. Sloane, <a href="/A321021/b321021.txt">Table of n, a(n) for n = 0..1000</a>

%p f:= proc(n) local F, S;

%p F:= convert(n, base, 10);

%p S:= select(t -> numboccur(t, F)>1, [$0..9]);

%p if S = {} then return n fi;

%p F:= subs(seq(s=NULL, s=S), F);

%p add(F[i]*10^(i-1), i=1..nops(F))

%p end proc: # A320486

%p x:=0: y:=1: lprint(x); lprint(y);

%p for n from 2 to 500 do

%p z:=f(x+y); lprint(z); x:=y; y:=z; od:

%Y Cf. A000045 (Fibonacci), A320486 (Angelini's contraction), A321022.

%K nonn,base

%O 0,4

%A _N. J. A. Sloane_, Nov 19 2018

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Last modified June 19 10:33 EDT 2021. Contains 345126 sequences. (Running on oeis4.)