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A184827 a(n) = largest k such that A000959(n+1) = A000959(n) + (A000959(n) mod k), or 0 if no such k exists.

%I A184827 #12 Mar 04 2018 05:50:35
%S A184827 0,0,5,5,11,9,17,19,29,29,31,37,47,39,59,65,65,71,71,71,81,87,93,99,
%T A184827 107,103,125,125,131,129,131,143,155,157,167,153,185,191,189,197,199,
%U A184827 203,215,215,227,233,233,223,257,255,261,263
%N A184827 a(n) = largest k such that A000959(n+1) = A000959(n) + (A000959(n) mod k), or 0 if no such k exists.
%C A184827 From the definition, a(n) = A000959(n) - A031883(n) if A000959(n) - A031883(n) > A031883(n), 0 otherwise where A000959 are the lucky numbers and A031883 are the gaps between lucky numbers.
%H A184827 Rémi Eismann, <a href="/A184827/b184827.txt">Table of n, a(n) for n = 1..10000</a>
%e A184827 For n = 1 we have A000959(1) = 1, A000959(2) = 3; there is no k such that 3 - 1 = 2 = (1 mod k), hence a(1) = 0.
%e A184827 For n = 3 we have A000959(3) = 7, A000959(4) = 9; 5 is the largest k such that 9 - 7 = 2 = (7 mod k), hence a(3) = 5; a(3) = 7 -2 = 5.
%e A184827 For n = 24 we have A000959(24) = 105, A000959(25) = 111; 99 is the largest k such that 111 - 105 = 6 = (105 mod k), hence a(24) = 99; a(24) = 105 - 6 = 99.
%Y A184827 Cf. A000959, A031883, A130889, A184828, A117078, A117563, A001223, A118534.
%K A184827 nonn,easy
%O A184827 1,3
%A A184827 _Rémi Eismann_, Jan 23 2011