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%I #34 May 05 2023 07:48:40
%S 4,5,6,8,19,48,124,323,844,2208,5779,15128,39604,103683,271444,710648,
%T 1860499,4870848,12752044,33385283,87403804,228826128,599074579,
%U 1568397608,4106118244,10749957123,28143753124,73681302248
%N Numbers having three 1's in their base-phi representation.
%H G. C. Greubel, <a href="/A104626/b104626.txt">Table of n, a(n) for n = 1..1000</a>
%H Jeffrey Shallit, <a href="https://arxiv.org/abs/2305.02672">Proving Properties of phi-Representations with the Walnut Theorem-Prover</a>, arXiv:2305.02672 [math.NT], 2023.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PhiNumberSystem.html">Phi Number System</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a>
%F {n: A055778(n) = 3}. - _R. J. Mathar_, Sep 05 2010
%F a(n) = Lucas(2*n-4) + 1, for n>3. - _Ralf Stephan_, Nov 13 2010
%t Join[{4, 5, 6}, Table[LucasL[2*n-4] + 1, {n, 4, 50}]] (* _G. C. Greubel_, Aug 13 2018 *)
%o (PARI) for(n=1,50, print1(if(n==1,4, if(n==2, 5, if(n==3, 6, 1 + fibonacci(2*n-3) + fibonacci(2*n-5)))), ", ")) \\ _G. C. Greubel_, Aug 13 2018
%o (Magma) [4,5,6] cat [1 + Fibonacci(2*n-3) + Fibonacci(2*n-5): n in [4..50]]; // _G. C. Greubel_, Aug 13 2018
%Y Cf. A005248, A104627, A104628, A065034.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Mar 17 2005
%E Terms 5 and 6 added by _Jaroslav Krizek_, May 25 2010
%E Edited by _R. J. Mathar_, Sep 05 2010
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