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

1,1

Comments

Drmota, Müllner, & Spiegelhofer prove that a(n) exists for each n, see links. - Charles R Greathouse IV, Oct 18 2021

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]

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A182561, A182535, A000040, A007895.

Sequence in context: A275209 A007049 A133407 * A067602 A216389 A154298

Adjacent sequences: A182664 A182665 A182666 * A182668 A182669 A182670

Keyword

nonn

Author

Alex Ratushnyak, Dec 23 2012

Extensions

a(14)-a(29) calculated from the data of A182561 by Amiram Eldar, Oct 19 2019

Status

approved