|
%I #15 Mar 04 2021 07:02:25
%S 3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,
%T 30,31,32,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
%U 54,55,56,57,58,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76
%N Numbers that are the sum of a prime number and a positive Fibonacci number.
%C This sequence is a subsequence of A132145 and is the complement of A132146.
%C Lee shows that this sequence has positive lower density. - _Charles R Greathouse IV_, Nov 02 2010
%C The lower density of this sequence is at least 0.0254905 (Liu and Xue, 2021). - _Amiram Eldar_, Mar 04 2021
%H T. D. Noe, <a href="/A132147/b132147.txt">Table of n, a(n) for n = 1..1000</a>
%H K. S. Enoch Lee, <a href="https://doi.org/10.1142/S1793042110003708">On the sum of a prime and a Fibonacci number</a>, International Journal of Number Theory, Vol. 6, No. 7 (2010), pp. 1669-1676; <a href="https://arxiv.org/abs/1011.0173">arXiv preprint</a>, arXiv:1011.0173 [math.NT], 2010.
%H Zhixin Liu and Mengyuan Xue, <a href="https://doi.org/10.1142/S1793042121500640">The sum of a prime and a Fibonacci number</a>, International Journal of Number Theory (2021).
%e 11 = 3+8 is a term since it is the sum of a prime number (3) and a Fibonacci number (8).
%t Take[Union[Flatten[Table[Fibonacci[n] + Prime[k], {n, 70}, {k, 70}]]], 70]
%o (PARI) is(n)=my(k,f); while((f=fibonacci(k++))<n, if(isprime(n-f), return(1))); 0 \\ _Charles R Greathouse IV_, Sep 14 2015
%Y Cf. A000040, A000045, A132145, A132146.
%K nonn
%O 1,1
%A _Tanya Khovanova_, Aug 12 2007
|
