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Search: id:A031165
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| A031165 |
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a(n) = p(n+3)-p(n) (p()=primes). |
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+0
2
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Comments from Jonathan Vos Post (jvospost2(AT)yahoo.com), 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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FORMULA
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a(n) = prime(n+3) - prime(n). a(n) = A000040(n+3) - A000040(n). - Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 22 2006
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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.
a(99) = prime(102) - prime(99) = 557 - 523 = 34. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 22 2006
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MAPLE
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ithprime(n+3)-ithprime(n);
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MATHEMATICA
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t = Array[Prime, 75]; Drop[t, 3] - Drop[t, -3] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000040, A001223, A007530, A031131, A115401.
Adjacent sequences: A031162 A031163 A031164 this_sequence A031166 A031167 A031168
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KEYWORD
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nonn,new
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AUTHOR
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Jeff Burch (jmburch(AT)osprey.smcm.edu)
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EXTENSIONS
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Edited by R. J. Mathar and njas, Aug 11 2008
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