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A036263
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Second differences of primes.
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19
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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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a(A064113(n)) = 0. [Reinhard Zumkeller, Jan 20 2012]
Conjecture: |a(1)|+|a(2)|+..+|a(n)| ~ prime(n). [Thomas Ordowski, Jul 21 2012]
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = prime(n) + prime(n+2) - 2*prime(n+1).
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EXAMPLE
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a(3) = 5 + 11 - 2*7 = 16 - 14 = 2.
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MATHEMATICA
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Table[ Prime[n - 1] + Prime[n + 1] - 2*Prime[n], {n, 2, 105}]
Differences[Prime[Range[100]], 2] (* Harvey P. Dale, Oct 14 2012 *)
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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
-- Reinhard Zumkeller, Oct 29 2011
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CROSSREFS
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Cf. A001223, A036262, A051635, A006562, A051634, A147812, A147813.
Sequence in context: A064136 A143526 A072924 * A168514 A060447 A118177
Adjacent sequences: A036260 A036261 A036262 * A036264 A036265 A036266
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KEYWORD
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sign,easy,nice
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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