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 A245070 Smallest positive non-divisor of the n-th Lucas number (A000032). 1
 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This sequence seems to be cyclic with period 12, but the equivalent sequence for the Fibonacci numbers (A152727) is not. Lucas numbers modulo 12 are cyclic with period 24 and no 0 in the cycle (unlike Fibonacci numbers): 2, 1, 3, 4, 7, 11, 6, 5, 11, 4, 3, 7, 10, 5, 3, 8, 11, 7, 6, 1, 7, 8, 3, 11. It follows that this sequence is cyclic with period 12: 3, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 2. - Jens Kruse Andersen, Jul 15 2014 LINKS Jens Kruse Andersen, Table of n, a(n) for n = 0..1000 FORMULA For n >= 12, a(n) = a(n-12). - Jens Kruse Andersen, Jul 15 2014 EXAMPLE a(6) = 4 because lucas(6) = 18, both 2 and 3 divide 18, but 4 does not. PROG (PARI) lucas(n) = if(n==0, 2, 2*fibonacci(n-1)+fibonacci(n)); vector(1000, n, m=lucas(n-1); d=2; while(m%d==0, d++); d) CROSSREFS Cf. A000032, A152727. Sequence in context: A052901 A127807 A122028 * A270226 A305534 A248138 Adjacent sequences:  A245067 A245068 A245069 * A245071 A245072 A245073 KEYWORD nonn AUTHOR Colin Barker, Jul 12 2014 STATUS approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)