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Smallest Fibonacci numbers with Factor 3^n.
1

%I #7 Mar 08 2023 13:25:35

%S 1,3,144,14930352,16641027750620563662096,

%T 23041483585524168262220906489642018075101617466780496790573690289968,

%U 61164766314391710035884829815943265224568052927769577329622759945237346639032672167677108820397521093126336764093707189513015791230614183821533954756601790054548991800671186110593262317807192235925106064

%N Smallest Fibonacci numbers with Factor 3^n.

%e f(1) = 3^0 = 1,

%e f(4) = 3^1 = 3,

%e f(12) = 2^4*3^2 = 144,

%e f(36) = 2^4*3^3*17*19*107 = 14930352,

%e f(108) = 2^4*3^4*17*19*53*107*109*5779*11128427,

%e f(324) = 2^4*3^5*17*19*53*107*109*2269*..,

%e f(972) = 2^4*3^6*17*19*53*107*109*2269*..., ..

%t lst={1};k=4;Do[AppendTo[lst,Fibonacci[k]];k*=3,{n,7}];lst

%Y Cf. A000045.

%K nonn

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Nov 19 2010