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A333839
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a(n) = Sum_{k = 4..n} ((prevprime(k) + nextprime(k))/2 - k).
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0
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0, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 2, 4, 5, 5, 4, 2, 0, 0, 2, 4, 5, 5, 4, 2, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 2, 4, 5, 5, 4, 2, 2, 4, 5, 5, 4, 2, 0, 0, 2, 4, 5, 5, 4, 2, 1, 2, 2, 1, 0, 0, 2, 4, 5, 5, 4, 2, 1, 2, 2, 1, 2, 4, 5, 5, 4, 2, 3, 6, 8, 9, 9, 8, 6
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OFFSET
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4,5
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COMMENTS
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It looks like a(n) >= 0 for all n >= 4.
If (n,n+2) are twin primes, then a(n) = 0 and a(n+1) = 0.
Partial sums of b(k) = prevprime(k) + nextprime(k) - 2*k; b(k) = 0 for A145025.
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LINKS
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FORMULA
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EXAMPLE
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a(4) = (3 + 5)/2 - 4 = 0;
a(5) = (3 + 5)/2 - 4 + (3 + 7)/2 - 5 = 0.
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MATHEMATICA
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Array[Sum[Total[NextPrime[k, {-1, 1}]]/2 - k, {k, 4, #}] &, 92, 4] (* Michael De Vlieger, Apr 10 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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