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A036263
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Second differences of primes.
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51
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1, 0, 2, -2, 2, -2, 2, 2, -4, 4, -2, -2, 2, 2, 0, -4, 4, -2, -2, 4, -2, 2, 2, -4, -2, 2, -2, 2, 10, -10, 2, -4, 8, -8, 4, 0, -2, 2, 0, -4, 8, -8, 2, -2, 10, 0, -8, -2, 2, 2, -4, 8, -4, 0, 0, -4, 4, -2, -2, 8, 4, -10, -2, 2, 10, -8, 4, -8, 2, 2, 2, -2, 0, -2, 2, 2, -4, 4, 2, -8, 8, -8, 4, -2, 2, 2, -4, -2, 2, 8, -4
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OFFSET
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1,3
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COMMENTS
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Conjecture: |a(1)| + |a(2)| + ... + |a(n)| ~ prime(n). - Thomas Ordowski, Jul 21 2012
Sum_{i = 2..n - 1} a(i) = prime(n + 1) - prime(n) - 2; Sum_{i = 2..n - 1} a(i) = 0 whenever prime(n) is a lesser of twin primes. - Hamdi Murat Yildirim, Jun 24 2014
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LINKS
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FORMULA
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a(n) = prime(n) + prime(n+2) - 2*prime(n+1). - Thomas Ordowski, Jul 21 2012
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EXAMPLE
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a(3) = 5 + 11 - 2*7 = 16 - 14 = 2.
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MAPLE
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MATHEMATICA
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Table[Prime[n - 1] + Prime[n + 1] - 2*Prime[n], {n, 2, 105}]
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PROG
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(PARI) for(n=2, 100, print1(prime(n+2)-2*prime(n+1)+prime(n)", "))
(Haskell)
a036263 n = a036263_list !! (n-1)
a036263_list = zipWith (-) (tail a001223_list) a001223_list
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CROSSREFS
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KEYWORD
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sign,easy,nice
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AUTHOR
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STATUS
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approved
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