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A080763 Exchange 1's and 2's in the eta-sequence A006337.

%I A080763 #23 Aug 04 2022 05:18:52
%S A080763 2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,1,2,2,1,2,1,2,
%T A080763 2,1,2,1,2,2,1,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,
%U A080763 2,1,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,1,2,2,1,2,1,2,2,1,2,1,2,1,2,2,1,2,1,2,2
%N A080763 Exchange 1's and 2's in the eta-sequence A006337.
%H A080763 T. D. Noe, <a href="/A080763/b080763.txt">Table of n, a(n) for n=1..10000</a>
%H A080763 N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)
%F A080763 Digits := 100: c2 := sqrt(2.): A080763 := n->3-floor((n+1)*c2)+floor(n*c2);
%t A080763 Flatten[ Table[ Nest[ Flatten[ # /. {1 -> {2, 2, 1}, 2 -> {2, 1}}] &, {2}, n], {n, 5}]] (* _Robert G. Wilson v_, May 06 2005 *)
%o A080763 (Python)
%o A080763 from math import isqrt
%o A080763 def A080763(n): return 3+isqrt(m:=n*n<<1)-isqrt(m+(n<<2)+2) # _Chai Wah Wu_, Aug 03 2022
%Y A080763 Different from A022921.
%Y A080763 The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A003151 as the parent: A003151, A001951, A001952, A003152, A006337, A080763, A082844 (conjectured), A097509, A159684, A188037, A245219 (conjectured), A276862. - _N. J. A. Sloane_, Mar 09 2021
%K A080763 nonn,easy
%O A080763 1,1
%A A080763 _N. J. A. Sloane_, Mar 25 2003