A182667 - OEIS

%I #26 Oct 18 2021 12:19:25

%S 2,7,17,53,197,373,983,3803,6709,17333,43783,103681,317789,785671,

%T 2177321,5581493,20632861,38770357,126491971,331160281,1070825143,

%U 1836305137,6643521067,10749957121,32951279111,86252640919,213265164691,591286712167,2126709216773

%N Smallest prime with n terms in its Zeckendorf representation.

%C Drmota, Müllner, & Spiegelhofer prove that a(n) exists for each n, see links. - _Charles R Greathouse IV_, Oct 18 2021

%H Amiram Eldar and Charles R Greathouse IV, <a href="/A182667/b182667.txt">Table of n, a(n) for n = 1..1000</a> (first 33 terms from Amiram Eldar)

%H Michael Drmota, Clemens Müllner, and Lukas Spiegelhofer, <a href="https://arxiv.org/abs/2109.04068">Primes as sums of Fibonacci numbers</a>, arXiv:2109.04068 [math.NT]

%F a(n) = A000040(A182561(n)).

%e The smallest prime with 3 terms in its Zeckendorf representation is a(3) = 17.

%e ... with 17 = Fib(7) +  Fib(4) + Fib(2) = 13 + 3 + 1. - _Bernard Schott_, Oct 19 2019

%o (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(t<b && isprime(t), b=t), 2)); b \\ _Charles R Greathouse IV_, Sep 21 2021

%Y Cf. A182561, A182535, A000040, A007895.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Dec 23 2012

%E a(14)-a(29) calculated from the data of A182561 by _Amiram Eldar_, Oct 19 2019