OFFSET
1,3
COMMENTS
If one takes L_k, for k >= 1, that is A000204, then a(1) = 1 and a(2) = 3 followed by the given numbers. This fits then with A106291(n) = A253808(n)*a(n), n >= 1 (where in A253808 a negative entry at position n indicates, as in the present sequence, that the Lucas numbers are not divisible by n. For odd primes not dividing any Lucas numbers see A053028. No power 2^m, m >= 3 divides any Lucas number, see, e.g., Vajda, p. 81). - Wolfdieter Lang, Jan 20 2015
REFERENCES
A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 25.
S. Vajda, Fibonacci and Lucas numbers and the Golden Section, Ellis Horwood Ltd., Chichester, 1989.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
EXAMPLE
a(9) = 6 because L_6 = 18 is the first number in the Lucas sequence (A000032) that 9 divides.
MATHEMATICA
test[n_] := Module[{a, b, t, cnt = 1}, {a, b} = {2, 1}; While[cnt++; t = b; b = Mod[a + b, n]; a = t; ! (b == 0 || {a, b} == {2, 1})]; If[b == 0, cnt, -1]]; Join[{0, 0}, Table[test[i], {i, Range[3, 100]}]] (* T. D. Noe, Mar 22 2013 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Casey Mongoven, Mar 20 2013
EXTENSIONS
Edited. Added "k >= 0" in the name and added cross references. - Wolfdieter Lang, Jan 20 2015
STATUS
approved