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

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

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 A374742 A023439

Adjacent sequences: A321018 A321019 A321020 * A321022 A321023 A321024

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 19 2018

Status

approved