A080120 Dyck path encodings of Legendre's candelabras formed for primes in A080114. (I.e., symmetric rooted plane trees constructed from their quadratic residue sets.)

10, 1010, 110100, 1011100010, 101100110010, 1111010110011001010000, 110110111100010101110000100100, 101100101111000100110111000010110010, 1111011110010101110010011011000101011000010000

Offset

1,1

Comments

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).

Links

Table of n, a(n) for n=1..9.

Antti Karttunen, Illustration of initial terms

Formula

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

Maple

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

Crossrefs

Same sequence in decimal: A080118. Cf. A080114.

Sequence in context: A176067 A080070 A303610 * A300571 A274069 A325493

Adjacent sequences: A080117 A080118 A080119 * A080121 A080122 A080123

Keyword

nonn

Author

Antti Karttunen, Feb 11 2003

Status

approved