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A068857 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).

%I A068857 #30 May 06 2024 11:04:41
%S A068857 0,8,24,48,288,16128,11950848,4636929024,88106288385024,
%T A068857 8038489644431643930624,15177535939786079616000991061008232448,
%U A068857 40096515501441989312471498490435884509054125751527350190658560000
%N A068857 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 A068857 Chai Wah Wu, <a href="/A068857/b068857.txt">Table of n, a(n) for n = 0..14</a>
%F A068857 a(n) = 8 * A068776(n-1) for n>=1.
%e A068857 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 A068857 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 A068857 (Python)
%o A068857 from itertools import islice
%o A068857 from sympy import sqrt_mod_iter
%o A068857 def A068857_gen(): # generator of terms
%o A068857     yield 0
%o A068857     a = 8
%o A068857     while True:
%o A068857         yield a
%o A068857         b = a+1
%o A068857         for d in sqrt_mod_iter(1,a):
%o A068857             if d==1 or d**2-1 == a:
%o A068857                 d += a
%o A068857             if d&1 and d < b:
%o A068857                 b = d
%o A068857         a = b**2-1
%o A068857 A068857_list = list(islice(A068857_gen(),11)) # _Chai Wah Wu_, May 05 2024
%Y A068857 Cf. A000217, A033996, A068776.
%K A068857 nonn
%O A068857 0,2
%A A068857 _Amarnath Murthy_, Mar 12 2002
%E A068857 More terms from _Sascha Kurz_, Mar 23 2002
%E A068857 a(8) onward corrected by _Sean A. Irvine_, Mar 18 2024
%E A068857 a(10)-a(11) from _Alois P. Heinz_, Mar 19 2024