A045895 - OEIS

%I #21 Sep 14 2022 02:00:23

%S 0,2,12,12,40,30,84,56,144,90,220,132,312,182,420,240,544,306,684,380,

%T 840,462,1012,552,1200,650,1404,756,1624,870,1860,992,2112,1122,2380,

%U 1260,2664,1406,2964,1560

%N Period length of pairs (a,b) where a has period 2n-2 and b has period n.

%H G. C. Greubel, <a href="/A045895/b045895.txt">Table of n, a(n) for n = 1..5000</a>

%H Ralf W. Grosse-Kunstleve, <a href="https://web.archive.org/web/20070603212504/http://cci.lbl.gov/~rwgk/EIS/Ceiling.html">Origin of EIS sequences A045895 & A045896</a>. [Wayback Machine copy]

%F a(n) = A204557(n) - A204556(n). - _Reinhard Zumkeller_, Jan 18 2012

%F From _Amiram Eldar_, Sep 14 2022: (Start)

%F a(n) = n*(n-1) for n even.

%F a(n) = 2*n*(n-1) for n odd.

%F a(n) = lcm(2*n-2, n).

%F a(n) = 2*A045896(n-2).

%F Sum_{n>=2} 1/a(n) = (log(2)+1)/2. (End)

%t Table[ LCM[ 2*n-2, n ], {n, 40} ]

%o (PARI) for(n=1, 50, print1(lcm(2*n-2, n), ", ")) \\ _G. C. Greubel_, Jun 15 2018

%o (Magma) [Lcm(2*n-2, n): n in [1..50]]; // _G. C. Greubel_, Jun 15 2018

%Y Cf. A045896, A204556, A204557.

%K nonn

%O 1,2

%A _Ralf W. Grosse-Kunstleve_