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A174348 Alternately multiply and divide, with a(1)=3 and a(1)=7.

%I A174348 #16 Sep 06 2020 15:51:10
%S A174348 3,7,21,3,63,21,1323,63,83349,1323,110270727,83349,9190954824723,
%T A174348 110270727,1013493270346362783621,9190954824723,
%U A174348 9314970862914194811435918430261983,1013493270346362783621
%N A174348 Alternately multiply and divide, with a(1)=3 and a(1)=7.
%H A174348 Robert Israel, <a href="/A174348/b174348.txt">Table of n, a(n) for n = 1..32</a>
%F A174348 From _Robert Israel_, Dec 05 2016: (Start)
%F A174348 a(2k) = a(2k-3) = 3^A000045(k-1)*7^A000045(k-2) for k >=2.
%F A174348 a(2k+1) = a(2k)*a(2k-1) = 3^A000045(k+1)*7^A000045(k) for k>=1. (End)
%p A174348 f:= proc(n) if n::even then 3^combinat:-fibonacci(n/2-1)*7^combinat:-fibonacci(n/2-2)
%p A174348             else 3^combinat:-fibonacci((n+1)/2)*7^combinat:-fibonacci((n-1)/2)
%p A174348             fi
%p A174348 end proc:
%p A174348 map(f, [$1..20]); # _Robert Israel_, Dec 05 2016
%t A174348 nxt[{a_,b_}]:={a*b,(a*b)/b}; NestList[nxt,{3,7},10]//Flatten (* _Harvey P. Dale_, Sep 06 2020 *)
%Y A174348 Cf. A000045, A115033, A115034, A115043.
%K A174348 nonn,easy
%O A174348 1,1
%A A174348 _Giovanni Teofilatto_, Mar 16 2010
%E A174348 a(18) corrected by _Robert Israel_, Dec 05 2016