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

Author

Antti Karttunen, Feb 11 2003

Keywords

• nonn

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

• Antti Karttunen, Illustration of initial terms

Crossrefs

Same sequence in decimal: A080118. Cf. A080114.

Programs

Maple

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

Formula

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