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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
 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, 73, 1, 74, 75, 149, 4, 153, 157, 310, 467, 0, 467, 467, 934, 40, 974, 4, 978, 982, 1960, 94, 2054, 2148, 40, 21, 61, 82, 143, 5, 148, 153, 301, 5, 306, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) = A320486(a(n-2)+a(n-1)). 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). 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). LINKS N. J. A. Sloane, Table of n, a(n) for n = 0..1000 MAPLE f:= proc(n) local F, S;   F:= convert(n, base, 10);   S:= select(t -> numboccur(t, F)>1, [\$0..9]);   if S = {} then return n fi;   F:= subs(seq(s=NULL, s=S), F);   add(F[i]*10^(i-1), i=1..nops(F)) end proc: # A320486 x:=0: y:=1: lprint(x); lprint(y); for n from 2 to 500 do z:=f(x+y); lprint(z); x:=y; y:=z; od: CROSSREFS Cf. A000045 (Fibonacci), A320486 (Angelini's contraction), A321022. Sequence in context: A175712 A013986 A121343 * A236768 A023439 A147660 Adjacent sequences:  A321018 A321019 A321020 * A321022 A321023 A321024 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Nov 19 2018 STATUS approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)