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a(n) = smallest k such that A014612(n+1) = A014612(n) + (A014612(n) mod k), or 0 if no such k exists.
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%I #6 Mar 31 2012 14:42:50

%S 0,0,4,13,2,13,18,4,43,8,3,41,4,4,3,13,2,37,16,43,97,4,9,10,53,4,5,10,

%T 3,6,61,43,2,11,2,12,163,8,13,2,5,173,8,89,4,3,37,61,101,101,107,229,

%U 113

%N a(n) = smallest k such that A014612(n+1) = A014612(n) + (A014612(n) mod k), or 0 if no such k exists.

%C a(n) is the "weight" of 3-almost primes.

%C The decomposition of 3-almost primes into weight * level + gap is A014612(n) = a(n) * A184753(n) + A114403(n) if a(n) > 0.

%H Remi Eismann, <a href="/A130650/b130650.txt">Table of n, a(n) for n=1..9999</a>

%e For n = 1 we have A014612(1) = 8, A014612(2) = 12; there is no k such that 12 - 8 = 4 = (8 mod k), hence a(1) = 0.

%e For n = 3 we have A014612(3) = 18, A014612(4) = 20; 4 is the smallest k such that 20 - 18 = 2 = (18 mod k), hence a(3) = 4.

%e For n = 21 we have A014612(21) = 98, A014612(22) = 99; 97 is the smallest k such that 99 - 98 = 1 = (97 mod k), hence a(21) = 97.

%Y Cf. A014612, A114403, A184753, A184752, A117078, A117563, A001223, A118534.

%K nonn

%O 1,3

%A _RĂ©mi Eismann_, Aug 16 2007 - Jan 21 2011