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A130889 a(n) = smallest k such that A000959(n+1) = A000959(n) + (A000959(n) mod k), or 0 if no such k exists.

%I A130889 #6 Mar 31 2012 14:42:50
%S A130889 0,0,5,5,11,9,17,19,29,29,31,37,47,13,59,5,5,71,71,71,9,29,31,9,107,
%T A130889 103,5,5,131,43,131,11,5,157,167,51,5,191,7,197,199,29,5,43,227,233,
%U A130889 233,223,257,15,9,263,281,281,281,97,13,59,317,7,17,17,47,11,353,71,349,379,389
%N A130889 a(n) = smallest k such that A000959(n+1) = A000959(n) + (A000959(n) mod k), or 0 if no such k exists.
%C A130889 a(n) is the "weight" of lucky numbers.
%C A130889 The decomposition of lucky numbers into weight * level + gap is A000959(n) = a(n) * A184828(n) + A031883(n) if a(n) > 0.
%H A130889 Remi Eismann, <a href="/A130889/b130889.txt">Table of n, a(n) for n=1..9999</a>
%e A130889 For n = 1 we have A000959(n) = 1, A000959(n+1) = 3; there is no k such that 3 - 1 = 2 = (1 mod k), hence a(1) = 0.
%e A130889 For n = 3 we have A000959(n) = 7, A000959(n+1) = 9; 5 is the smallest k such that 9 - 7 = 2 = (7 mod k), hence a(3) = 5.
%e A130889 For n = 24 we have A000959(n) = 105, A000959(n+1) = 111; 9 is the smallest k such that 111 - 105 = 6 = (105 mod k), hence a(24) = 9.
%Y A130889 Cf. A000959, A031883, A184828, A184827, A117078, A117563, A001223, A118534.
%K A130889 nonn
%O A130889 1,3
%A A130889 _Rémi Eismann_, Aug 21 2007 - Jan 23 2011