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A136612
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a(n) = ((prime(n+3) + prime(n+1)) - (prime(n+2) + prime(n))).
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2
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3, 6, 4, 8, 4, 8, 8, 6, 12, 6, 8, 8, 8, 10, 8, 12, 6, 8, 10, 6, 12, 12, 10, 10, 8, 4, 8, 16, 8, 20, 6, 16, 4, 16, 8, 10, 12, 10, 8, 16, 4, 14, 4, 16, 14, 16, 14, 8, 8, 6, 16, 8, 16, 12, 8, 12, 6, 8, 14, 16, 14, 16, 8, 16, 10, 24, 8, 14, 8, 12, 12, 14, 10, 12, 12, 10, 16, 14, 10, 20, 4, 16, 6
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OFFSET
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1,1
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COMMENTS
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a(n) is the sum of two prime gaps, thus a(n) >= 4 for n > 1. Conjecturally a(n) << log^2 n (probably with constant around 2). - Charles R Greathouse IV, Aug 25 2014
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LINKS
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FORMULA
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EXAMPLE
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2 + 5 = 7
3 + 7 = 10
5 + 11 = 16
7 + 13 = 20
...
so the sequence is: 10 - 7 = 3,
16 - 10 = 6,
20 - 16 = 4,
28 - 20 = 8,
...
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MAPLE
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MATHEMATICA
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#[[4]]+#[[2]]-#[[3]]-#[[1]]&/@Partition[Prime[Range[90]], 4, 1] (* Harvey P. Dale, May 15 2013 *)
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PROG
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(PARI) a(n)=my(p=prime(n), q=nextprime(p+1), r=nextprime(q+1)); nextprime(r+1)-r + q-p \\ Charles R Greathouse IV, Aug 25 2014
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CROSSREFS
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KEYWORD
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easy,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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