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0, 0, 1, 0, 3, 1, 5, 3, 1, 9, 1, 3, 13, 3, 1, 1, 19, 5, 9, 23, 1, 15, 11, 9, 3, 33, 11, 35, 21, 3, 3, 5, 45, 3, 49, 5, 1, 3, 23, 1, 59, 9, 63, 27, 65, 11, 1, 3, 75, 45, 1, 79, 21, 35, 1, 1, 89, 5, 39, 93, 21, 9, 3, 103, 3, 3, 25, 3, 115, 69, 1, 39, 19, 1, 75, 29, 3, 3, 3, 21, 139, 3, 143, 61, 87
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OFFSET
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1,5
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COMMENTS
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a(n) is the "level" of prime(n).
There is a unique decomposition of the primes: provided the level a(n) is > 0, we have prime(n) = weight * level + gap, or A000040(n)=A117078(n)*a(n)+A001223(n).
a(n) = 0 only for primes 2, 3 and 7.
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LINKS
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EXAMPLE
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a(7)=15/3=5; a(14)=39/13=3; a(16)=47/47=1; a(18)=55/11=5; a(29)=105/5=11.
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MATHEMATICA
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a34[n_] := If[n == 1 || n == 2 || n == 4, 0, 2 Prime[n] - Prime[n+1]];
a78[n_] := Block[{a, p = Prime[n], np = Prime[n+1]}, a = Min[Select[ Divisors[2p - np], # > np - p& ]]; If[a == Infinity, 0, a]];
a[n_] := If[a78[n] == 0, 0, a34[n]/a78[n]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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