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A031165
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a(n) = prime(n+3) - prime(n).
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17
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5, 8, 8, 10, 8, 10, 12, 12, 14, 12, 12, 10, 12, 16, 14, 14, 12, 12, 12, 12, 16, 18, 18, 14, 10, 8, 10, 20, 22, 24, 12, 18, 14, 18, 14, 16, 16, 16, 14, 18, 14, 16, 8, 18, 26, 28, 18, 10, 12, 12, 18, 18, 22, 18, 14, 14, 12, 12, 16, 26, 28, 20, 10, 20, 24, 30, 18, 16, 12
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Comments from Jonathan Vos Post, Jan 22 2006 (Start): This sequence is the k=3 case of the family of sequences a(k,n) = prime(n+k) - prime(n). See A001223 and A031131 for k = 1 and 2.
The records in this sequence give A115401. The minimal value, after the anomalous initial values (5, 8, 8), is 8 which occurs iff n is an element of A007530 (prime quadruples: numbers n such that n, n+2, n+6, n+8 are all prime). (End)
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LINKS
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FORMULA
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EXAMPLE
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a(1) = prime(4) - prime(1) = 7 - 2 = 5, which is the only odd element of this sequence.
a(2) = prime(5) - prime(2) = 11 - 3 = 8.
a(3) = prime(6) - prime(3) = 13 - 5 = 8.
a(4) = prime(7) - prime(4) = 17 - 7 = 10.
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MAPLE
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a:= n-> ithprime(n+3)-ithprime(n): seq (a(n), n=1..80);
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MATHEMATICA
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#[[4]]-#[[1]]&/@Partition[Prime[Range[80]], 4, 1] (* Harvey P. Dale, Nov 07 2021 *)
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PROG
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(Magma) [NthPrime(n+3)-NthPrime(n): n in [1..100] ]; // Vincenzo Librandi, Apr 11 2011
(Haskell)
a031165 n = a031165_list !! (n-1)
a031165_list = zipWith (-) (drop 3 a000040_list) a000040_list
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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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