A354158 The Bodlaender function: a(1) = -1; a(2*n) = a(n), a(2*n+1) = a(n+1) + n.

-1, -1, 0, -1, 2, 0, 2, -1, 6, 2, 5, 0, 8, 2, 6, -1, 14, 6, 11, 2, 15, 5, 11, 0, 20, 8, 15, 2, 20, 6, 14, -1, 30, 14, 23, 6, 29, 11, 21, 2, 35, 15, 26, 5, 33, 11, 23, 0, 44, 20, 33, 8, 41, 15, 29, 2, 48, 20, 35, 6, 44, 14, 30, -1, 62, 30, 47, 14, 57, 23, 41, 6, 65, 29, 48, 11, 59, 21, 41, 2, 75, 35, 56, 15, 68, 26, 48, 5, 77, 33

Offset

1,5

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Hans L. Bodlaender, Jitender S. Deogun, Klaus Jansen, Ton Kloks, Dieter Kratsch, Haiko Müller, and Zsolt Tuza, Rankings of Graphs, SIAM J. Discrete Math., 11 (1998), 168-181. See p. 179.

Andreas M. Hinz, Sandi Klavžar, and Sara Sabrina Zemljič, A survey and classification of Sierpiński-type graphs, Discrete Applied Math., 217 (2017), 565-600. See Cor. 4.9.

Maple

g:=proc(n) option remember; if n = 1 then -1 elif (n mod 2) = 0 then g(n/2) else (n-1)/2 + g((n+1)/2); fi; end;

Prog

(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def a(n):
    if n == 1: return -1
    return a(n//2+1) + n//2 if n&1 else a(n//2)
print([a(n) for n in range(1, 91)]) # Michael S. Branicky, Jul 25 2022

Crossrefs

Sequence in context: A036997 A116900 A254372 * A363580 A196517 A298141

Adjacent sequences: A354155 A354156 A354157 * A354159 A354160 A354161

Keyword

sign

Author

N. J. A. Sloane, May 30 2022, following a suggestion from Don Knuth

Status

approved