login
Indices k >= 8 designating the k-Somos sequences that first become nonintegral at odd-indexed terms (i.e., positions of odd terms in A030127).
1

%I #15 Mar 05 2023 12:39:51

%S 8,9,13,16,19,20,25,27,32,37,40,53,61,64,73,80,97,104,114,128,133,134,

%T 177,205,209,232,272,275,395,486,920,991,1174,1195,1609,1612,1707,

%U 1734,1856,2168,2313,2409,2896,3136,3857,4753,5503,6289

%N Indices k >= 8 designating the k-Somos sequences that first become nonintegral at odd-indexed terms (i.e., positions of odd terms in A030127).

%C When k is in this sequence, the k-Somos sequence first becomes nonintegral at 2*k + 1; otherwise, the k-Somos sequence first becomes nonintegral at 2*k (conjecture).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SomosSequence.html">Somos Sequence</a>.

%e The k-Somos sequence obeys the recurrence:

%e S(n) = ( Sum_{j=1..floor(k/2)} S(n-j)*S(n-k+j) )/S(n-k),

%e with S(0) = S(1) = ... = S(k-1) = 1.

%Y Cf. A030127.

%K nonn

%O 1,1

%A _Paul D. Hanna_, Dec 08 2004

%E More terms from _David Wasserman_, Apr 03 2008