A182667 Smallest prime with n terms in its Zeckendorf representation.
2, 7, 17, 53, 197, 373, 983, 3803, 6709, 17333, 43783, 103681, 317789, 785671, 2177321, 5581493, 20632861, 38770357, 126491971, 331160281, 1070825143, 1836305137, 6643521067, 10749957121, 32951279111, 86252640919, 213265164691, 591286712167, 2126709216773
Offset: 1
Keywords
Examples
The smallest prime with 3 terms in its Zeckendorf representation is a(3) = 17. ... with 17 = Fib(7) + Fib(4) + Fib(2) = 13 + 3 + 1. - _Bernard Schott_, Oct 19 2019
Links
- Amiram Eldar and Charles R Greathouse IV, Table of n, a(n) for n = 1..1000 (first 33 terms from Amiram Eldar)
- Michael Drmota, Clemens Müllner, and Lukas Spiegelhofer, Primes as sums of Fibonacci numbers, arXiv:2109.04068 [math.NT]
Programs
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PARI
a(n)=my(b=oo,k); while(b==oo, k++; forvec(v=vector(n,i,[1,n+k]), my(t=sum(i=1,n,fibonacci(i+v[i]))); if(tCharles R Greathouse IV, Sep 21 2021
Extensions
a(14)-a(29) calculated from the data of A182561 by Amiram Eldar, Oct 19 2019
Comments