

A164816


Prime factors in a divisibility sequence of the Lucas sequence v(P=3,Q=5) of the second kind.


0



2, 3, 17, 103, 163, 373, 487, 1733, 3469, 4373, 10259, 35153
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OFFSET

1,1


COMMENTS

This is the last sequence on p. 15 of Smyth. The Lucas sequence with P = 3, Q = 5 is defined as v=2,3,1,18,49,57,.. where v(n) = P*v(n1)Q*v(n2), with g.f. (23x)/(13x+5x^2).
The indices n such that nv(n) define the sequence T = 1,3,9,27,81,153,243,459,... as listed by Smyth.
The OEIS sequence shows all distinct prime factors of elements of T.


LINKS



MAPLE

a := {2} ;
v := proc(n)
option remember;
if n <= 1 then
op(n+1, [2, 3]) ;
else
3*procname(n1)5*procname(n2) ;
end if;
end proc:
for n from 1 do
if modp(v(n), n) = 0 then
a := a union numtheory[factorset](n) ;
print(a);
end if;


MATHEMATICA

nmax = 10^7; v1 = 2; v2 = 3; s = {2}; For[n = 2, n <= nmax, n++, v3 = 3*v2  5*v1; v1 = v2; v2 = v3; If[Divisible[v3, n], u = Union[s, FactorInteger[n][[All, 1]] ]; If[u != s, s = u; Print["n = ", n, ", s = ", s]]]]; s (* JeanFrançois Alcover, Dec 08 2017 *)


CROSSREFS



KEYWORD

more,nonn


AUTHOR



EXTENSIONS

More detailed definition, comments rephrased, nonascii characters in URL's removed  R. J. Mathar, Sep 09 2009


STATUS

approved



