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A290263 Positive integers n such that the Zeckendorf (Fibonacci) representation of n^2 consists of two consecutive identical blocks. 1
4, 49, 306, 728, 2021, 3556, 3740, 5236, 21360, 35244, 98210, 243252, 1096099, 1625040, 1662860, 4976785, 5080514, 11408968, 31622994, 31831002, 33587514, 33599070, 56568930, 78167976, 209645093, 218297737, 220158358, 223289647, 225150268, 238764568, 535850484 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

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.

LINKS

Lars Blomberg, Table of n, a(n) for n = 1..47

Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations, preprint arXiv:1707.03894 [math.NT], July 14 2017.

EXAMPLE

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

PROG

(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

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

CROSSREFS

Cf. A014417.

Sequence in context: A163944 A000596 A113525 * A224538 A064751 A045787

Adjacent sequences:  A290260 A290261 A290262 * A290264 A290265 A290266

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Jul 25 2017

EXTENSIONS

a(23)-a(31) from Lars Blomberg, Aug 02 2017

STATUS

approved

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Last modified July 23 19:17 EDT 2021. Contains 346259 sequences. (Running on oeis4.)