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A290263 Positive integers n such that the Zeckendorf (Fibonacci) representation of n^2 consists of two consecutive identical blocks. 1

%I

%S 4,49,306,728,2021,3556,3740,5236,21360,35244,98210,243252,1096099,

%T 1625040,1662860,4976785,5080514,11408968,31622994,31831002,33587514,

%U 33599070,56568930,78167976,209645093,218297737,220158358,223289647,225150268,238764568,535850484

%N Positive integers n such that the Zeckendorf (Fibonacci) representation of n^2 consists of two consecutive identical blocks.

%D Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations, Experimental Math, 28 (2019), 428-439.

%H Lars Blomberg, <a href="/A290263/b290263.txt">Table of n, a(n) for n = 1..47</a>

%H Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, <a href="https://arxiv.org/abs/1707.03894">The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations</a>, preprint arXiv:1707.03894 [math.NT], July 14 2017.

%e For example, for n = 4, we have n^2 in Fibonacci representation is 100100, which consists of two consecutive blocks of 100.

%o (PARI) Z(n)=my(k=0, v, m); while(fibonacci(k)<=n, k=k+1); m=k-1; v=vector(m-1); v[1]=1; n=n-fibonacci(k-1); while(n>0, k=0; while(fibonacci(k)<=n, k=k+1); v[m-k+2]=1; n=n-fibonacci(k-1)); v; \\ after A014417

%o isok(n) = {my(vz = Z(n^2)); if (!(#vz % 2), vector(#vz/2, k, vz[k]) == vector(#vz/2, k, vz[k+#vz/2]););} \\ _Michel Marcus_, Aug 02 2017

%Y Cf. A014417.

%K nonn

%O 1,1

%A _Jeffrey Shallit_, Jul 25 2017

%E a(23)-a(31) from _Lars Blomberg_, Aug 02 2017

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Last modified September 20 08:10 EDT 2021. Contains 347577 sequences. (Running on oeis4.)