OFFSET
0,3
LINKS
Harry J. Smith, Table of n, a(n) for n=0..100
Larry Ericksen, Primality Testing and Prime Constellations, Šiauliai Mathematical Seminar, Vol. 3 (11), 2008. Mentions this sequence.
S. Litsyn and V. Shevelev, Irrational Factors Satisfying the Little Fermat Theorem, International Journal of Number Theory, vol.1, no.4 (2005), 499-512.
V. Shevelev, A property of n-bonacci constant, Seqfan (Mar 23 2014)
FORMULA
a(n) = (round(phi^prime(n+1)) - 1)/prime(n+1), where phi is golden ratio (A001622). Indeed, L(p) = round(phi^p), and round(phi^p) == 1 (mod p) and, what is more, for p>=5, round(phi^p) == 1 (mod 2*p) (see Shevelev link). In particular, all terms >=2 are even. - Vladimir Shevelev, Mar 24 2014
EXAMPLE
a(0) = (Lucas(2) - 1)/2 = (3 - 1)/2 = 1; a(3) = (Lucas(7) - 1)/7 = (29 - 1)/7 = 4.
MAPLE
MATHEMATICA
Array[(LucasL@ Prime@ # - 1)/Prime@ # &, {23}] (* Michael De Vlieger, Aug 22 2015 *)
PROG
(PARI) lucas(n) = if(n==0, 2, if(n==1, 1, fibonacci(n+1)+fibonacci(n-1)))
forprime(n=1, 100, print1((lucas(n)-1)/n, ", "))
(PARI) lucas(n)= { if(n==0, 2, if(n==1, 1, fibonacci(n + 1) + fibonacci(n - 1))) } { n=-1; forprime (p=2, prime(101), write("b064723.txt", n++, " ", (lucas(p) - 1)/p) ) } \\ Harry J. Smith, Sep 23 2009
(Magma) [(Lucas(NthPrime(n))-1)/NthPrime(n): n in [1..40]]; // Vincenzo Librandi, Aug 22 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Shane Findley, Oct 13 2001
EXTENSIONS
More terms from James A. Sellers and Klaus Brockhaus, Oct 16 2001
STATUS
approved