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A068859 a(1) = 3 = 1*3; a(n) = smallest multiple of a(n-1) which is of the form k(k+2).

%I A068859 #13 May 06 2024 11:04:21
%S A068859 3,15,120,360,5040,201600,256032000,4064251968000,
%T A068859 1024126980000259968000,29365589556381243259975904529351552000,
%U A068859 82421263677202543043706796882184010324019881962069201381742720000
%N A068859 a(1) = 3 = 1*3; a(n) = smallest multiple of a(n-1) which is of the form k(k+2).
%H A068859 Chai Wah Wu, <a href="/A068859/b068859.txt">Table of n, a(n) for n = 1..13</a>
%e A068859 120 = 10*12 belongs to this sequence and 360 = 18*20 is the smallest such multiple of 120.
%o A068859 (Python)
%o A068859 from itertools import islice
%o A068859 from sympy import sqrt_mod_iter
%o A068859 def A068859_gen(): # generator of terms
%o A068859     a = 3
%o A068859     while True:
%o A068859         yield a
%o A068859         b = a+1
%o A068859         for d in sqrt_mod_iter(1,a):
%o A068859             if d==1 or d**2-1 == a:
%o A068859                 d += a
%o A068859             if d < b:
%o A068859                 b = d
%o A068859         a = b**2-1
%o A068859 A068859_list = list(islice(A068859_gen(),11)) # _Chai Wah Wu_, May 05 2024
%Y A068859 Cf. A068857, A068858.
%K A068859 nonn
%O A068859 1,1
%A A068859 _Amarnath Murthy_, Mar 12 2002
%E A068859 More terms from _Sascha Kurz_, Mar 23 2002
%E A068859 Edited by _Don Reble_, Sep 12 2003