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Dyck path encodings of Legendre's candelabras formed for primes in A080114. (I.e., symmetric rooted plane trees constructed from their quadratic residue sets.)
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%I #10 Sep 20 2022 11:07:20

%S 10,1010,110100,1011100010,101100110010,1111010110011001010000,

%T 110110111100010101110000100100,101100101111000100110111000010110010,

%U 1111011110010101110010011011000101011000010000

%N Dyck path encodings of Legendre's candelabras formed for primes in A080114. (I.e., symmetric rooted plane trees constructed from their quadratic residue sets.)

%C For the 2nd, 5th and 8th term of the sequence, the quadratic residue set of the corresponding prime (5,13,37, of the form 4k+1) has been converted from symmetric to complementarily symmetric as 1001->1010, 101100001101->101100110010, 101100101111000100001000111101001101->101100101111000100110111000010110010, for the others (of the form 4k+3), it is the quadratic residue set encoded as in A055094 (with +1 mapped to 1 and -1 to 0).

%H Antti Karttunen, <a href="/A080120/a080120.pdf">Illustration of initial terms</a>

%F a(n) = A063171(A080119(n)).

%p A080120 := n -> convert(A080118(n),binary);

%Y Same sequence in decimal: A080118. Cf. A080114.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 11 2003