cp's OEIS Frontend

A068858 a(1) = 3 = 1*3; a(n) = smallest multiple of a(n-1) which is a product of two consecutive odd numbers.

%I A068858 #18 May 06 2024 11:04:17
%S A068858 3,15,195,4095,2477475,448422975,19384876786275,
%T A068858 70676639845770308825475,11604095937711402889585984522057770447375,
%U A068858 56023729629975618843823135187551800751351023283966800458449243286895375
%N A068858 a(1) = 3 = 1*3; a(n) = smallest multiple of a(n-1) which is a product of two consecutive odd numbers.
%C A068858 The multiple is assumed to be nontrivial, i.e. a(n) > a(n-1) as otherwise all terms are equal to 3. - _Chai Wah Wu_, May 05 2024
%H A068858 Chai Wah Wu, <a href="/A068858/b068858.txt">Table of n, a(n) for n = 1..12</a>
%e A068858 195 = 13*15 belongs to this sequence and the smallest multiple of 195 which is a product of two consecutive odd numbers is 4095 = 63*65.
%p A068858 f:= proc(x) local V,V1,y;
%p A068858      V:= map(t -> rhs(op(t))-1, [msolve(r^2=1,x)]);
%p A068858      V:= map(t -> `if`(t*(t+2)=x, t + x, t), V);
%p A068858      y:= min(map(t -> `if`(t::even, t+x, t), V));
%p A068858      y*(y+2)
%p A068858 end proc:
%p A068858 A[1]:= 3:
%p A068858 for n from 2 to 11 do A[n]:= f(A[n-1]) od:
%p A068858 seq(A[i],i=1..11); # _Robert Israel_, May 14 2017
%o A068858 (Python)
%o A068858 from itertools import islice
%o A068858 from sympy import sqrt_mod_iter
%o A068858 def A068858_gen(): # generator of terms
%o A068858     a = 3
%o A068858     while True:
%o A068858         yield a
%o A068858         b = a+1
%o A068858         for d in sqrt_mod_iter(1,a):
%o A068858             if d**2-1 == a:
%o A068858                 d += a
%o A068858             if d&1:
%o A068858                 d += a
%o A068858             if d < b:
%o A068858                 b = d
%o A068858         a = b**2-1
%o A068858 A068858_list = list(islice(A068858_gen(),11)) # _Chai Wah Wu_, May 05 2024
%Y A068858 Cf. A068857.
%K A068858 nonn
%O A068858 1,1
%A A068858 _Amarnath Murthy_, Mar 12 2002
%E A068858 More terms from _Sascha Kurz_, Mar 23 2002
%E A068858 Corrected by _Robert Israel_, May 14 2017