OFFSET
0,2
COMMENTS
The primes in this entirely odd sequence begin 3, 7, 13, 17, 19, 23, 29. By the theorems in Banks, there are an infinite number of primes in this sequence.
LINKS
William D. Banks, Igor E. Shparlinski, Prime numbers with Beatty sequences, arXiv:0708.1015 [math.NT], 7 Aug 2007.
FORMULA
a(n) = 1+2*floor(n*phi), where phi = (1 + sqrt(5))/2.
EXAMPLE
a(0) = 1 + 2*floor(0*phi) = 1 + 2*0 = 1.
a(1) = 1 + 2*floor(1*phi) = 1 + 2*floor(1.6180) = 1 + 2*1 = 3.
a(2) = 1 + 2*floor(2*phi) = 1 + 2*floor(3.2360) = 1 + 2*3 = 7.
a(3) = 1 + 2*floor(3*phi) = 1 + 2*floor(4.8541) = 1 + 2*4 = 9.
a(4) = 1 + 2*floor(4*phi) = 1 + 2*floor(6.4721) = 1 + 2*6 = 13.
a(5) = 1 + 2*floor(5*phi) = 1 + 2*floor(8.0901) = 1 + 2*8 = 17.
a(6) = 1 + 2*floor(6*phi) = 1 + 2*floor(9.7082) = 1 + 2*9 = 19.
a(7) = 1 + 2*floor(7*phi) = 1 + 2*floor(11.3262) = 1 + 2*11 = 23.
a(8) = 1 + 2*floor(8*phi) = 1 + 2*floor(12.9442) = 1 + 2*12 = 25.
a(9) = 1 + 2*floor(9*phi) = 1 + 2*floor(14.5623) = 1 + 2*14 = 29.
a(10) = 1 + 2*floor(10*phi) = 1 + 2*floor(16.1803) = 1 + 2*16 = 33.
MATHEMATICA
Table[1 + 2*Floor[n*(Sqrt[5] + 1)/2], {n, 0, 80}] (* Stefan Steinerberger, Aug 10 2007 *)
PROG
(Magma) [1+2*Floor(n*((1+Sqrt(5))/2)): n in [0..60]]; // Vincenzo Librandi, Sep 17 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Aug 09 2007
EXTENSIONS
More terms from Stefan Steinerberger, Aug 10 2007
STATUS
approved