A347325 Solution to the spectator-first Tantalizer problem.

1, 2, 2, 2, 2, 4, 4, 6, 6, 8, 8, 6, 6, 8, 8, 6, 6, 8, 8, 6, 6, 8, 8, 14, 14, 16, 16, 14, 14, 16, 16, 22, 22, 24, 24, 22, 22, 24, 24, 30, 30, 32, 32, 30, 30, 32, 32, 22, 22, 24, 24, 22, 22, 24, 24, 30, 30, 32, 32, 30, 30, 32, 32, 22, 22, 24, 24, 22, 22, 24, 24

Offset

1,2

Links

Marc Kouyoumdjian, Table of n, a(n) for n = 1..10000

Wei-Tung Chuang, Hong-Bin Chen and Fu-Yuen Hsiao, General solution to the spectator-first Tantalizer problem, Disc. Math. (2021) Vol. 344, No. 10, 112515. Gives first 100 terms.

Yiwei Zhang, C 1 line solution with explanation.

Formula

a(n) = 2 * (floor(n/2) + 1 - a(floor(n/2))) for n > 1. See Zhang's solution. - Zirui Wang, Jan 02 2022

Prog

(Python)
def A347325(n):
    a = [i for i in range(1, n+1)]
    while len(a) != 1:
        del a[:len(a)+1:2]
        a.reverse()
    return a[-1] # Marc Kouyoumdjian, Dec 15 2021
(Python)
def a(n):
    return 1 if n <= 1 else 2 * (n // 2 + 1 - a(n // 2))
# See Zhang's solution. - Zirui Wang, Jan 02 2022
(Python)
from math import log, log2
def A347325(n):
    return (-2) ** int(log2(n)) // 3 + 1 + (n & int('a' * int(log(n, 16) + 1), 16))
# Zirui Wang, Jan 03 2022
(PARI) a(n)={my(s=1, v=0); while(n>1, n=n\2; s=-2*s; v-=s*(1+n)); v+s} \\ Andrew Howroyd, Jan 02 2022

Crossrefs

Sequence in context: A349388 A347663 A071809 * A324762 A104976 A325710

Adjacent sequences: A347322 A347323 A347324 * A347326 A347327 A347328

Keyword

nonn

Author

N. J. A. Sloane, Sep 13 2021

Status

approved