A068857 - OEIS

%I #30 May 06 2024 11:04:41

%S 0,8,24,48,288,16128,11950848,4636929024,88106288385024,

%T 8038489644431643930624,15177535939786079616000991061008232448,

%U 40096515501441989312471498490435884509054125751527350190658560000

%N a(0) = 0, a(1) = 8; for n>=2: a(n) = smallest multiple of a(n-1) which is of the form 2k*(2k+2).

%H Chai Wah Wu, <a href="/A068857/b068857.txt">Table of n, a(n) for n = 0..14</a>

%F a(n) = 8 * A068776(n-1) for n>=1.

%e 24 = 4*6 is a member and the smallest multiple of 24 which is of the form 2k(2k+2) is 48 = 6*8.

%t m = 0; {0} ~Join~ Rest@ NestList[(m++; While[! Divisible[Set[k, # (# + 2) &[2 m]], #], m++]; k) &, 1, 8] (* _Michael De Vlieger_, Mar 18 2024 *)

%o (Python)

%o from itertools import islice

%o from sympy import sqrt_mod_iter

%o def A068857_gen(): # generator of terms

%o     yield 0

%o     a = 8

%o     while True:

%o         yield a

%o         b = a+1

%o         for d in sqrt_mod_iter(1,a):

%o             if d==1 or d**2-1 == a:

%o                 d += a

%o             if d&1 and d < b:

%o                 b = d

%o         a = b**2-1

%o A068857_list = list(islice(A068857_gen(),11)) # _Chai Wah Wu_, May 05 2024

%Y Cf. A000217, A033996, A068776.

%K nonn

%O 0,2

%A _Amarnath Murthy_, Mar 12 2002

%E More terms from _Sascha Kurz_, Mar 23 2002

%E a(8) onward corrected by _Sean A. Irvine_, Mar 18 2024

%E a(10)-a(11) from _Alois P. Heinz_, Mar 19 2024