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Search: id:A053597
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| A053597 |
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Let p(i) = i-th prime (A000040), let d(i) = p(i+1)-p(i) (A001223); a(n) = number of distinct numbers among d(n), d(n+1), d(n+2), ... before first duplicate is encountered. |
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3
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| 2, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 2, 3, 3, 3, 3, 2, 3, 4, 3, 2, 2, 2, 3, 2, 5, 4, 3, 2, 3, 2, 1, 2, 2, 1, 3, 2, 3, 2, 3, 2, 1, 3, 2, 3, 4, 3, 3, 2, 1, 1, 2, 3, 5, 4, 4, 4, 3, 2, 5, 5, 5, 4, 5, 4, 3, 2, 2, 1, 2, 3, 3, 2, 4, 3, 2, 2, 4, 3, 2, 3, 4, 3, 2, 4, 3, 3, 2, 2, 6, 5, 4, 5, 4, 3, 2, 2, 1, 2, 3, 2
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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The d sequence starting at p(7) = 17 is d(7) = 2, d(8) = 4, d(9) = 6, d(10) = 2, with three numbers before the first duplication, so a(7) = 3.
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MATHEMATICA
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f[n_] := Block[{k = 1}, While[p = Table[ Prime[i], {i, n, n + k}]; Length[ Union[ Drop[p, 1] - Drop[p, -1]]] == k, k++ ]; k - 1]; Table[ f[n], {n, 1, 105}]
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CROSSREFS
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A078515 gives RECORDS transform of this sequence. See also A079007.
Sequence in context: A086376 A160089 A129363 this_sequence A094570 A002375 A045917
Adjacent sequences: A053594 A053595 A053596 this_sequence A053598 A053599 A053600
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 07 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 07 2002
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