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Search: id:A075772
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| A075772 |
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Difference between n-th perfect power and the closest perfect power. |
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+0
6
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| 3, 3, 1, 1, 7, 2, 2, 4, 4, 13, 15, 17, 19, 4, 3, 3, 16, 25, 20, 9, 9, 13, 13, 33, 19, 18, 18, 39, 41, 28, 17, 17, 47, 49, 51, 53, 55, 57, 59, 39, 24, 24, 65, 67, 69, 35, 35, 38, 75, 77, 79, 47, 36, 36, 85, 87, 23, 23, 68, 10, 10, 12, 95, 97, 99, 101, 40, 40, 65, 107, 100, 11, 11
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Let {b(n)} be the sequence of perfect powers (A001597); then a(n) = min { b(n)-b(n-1), b(n+1)-b(n) }.
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EXAMPLE
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The perfect powers are 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, etc. The 7th is 27. This is 2 larger than the 6th (25) and 5 smaller than the 8th (32). So a(7)=2.
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MATHEMATICA
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pp = {-2, 1}; Do[ If[ !PrimeQ[n] && Apply[GCD, Last[ Transpose[ FactorInteger[n]]]] > 1, pp = Append[pp, n]], {n, 2, 10^4}]; Table[ Min[pp[[n + 1]] - pp[[n]], pp[[n + 2]] - pp[[n + 1]]], {n, 1, 75}]
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CROSSREFS
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Cf. A001597, A053289, A075773.
Sequence in context: A083029 A084546 A026515 this_sequence A142157 A119608 A101842
Adjacent sequences: A075769 A075770 A075771 this_sequence A075773 A075774 A075775
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KEYWORD
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nonn
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AUTHOR
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N. Fernandez (primeness(AT)borve.org), Oct 09 2002
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and John W. Layman (layman(AT)math.vt.edu), Oct 10 2002
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