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Search: id:A051699
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| A051699 |
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Distance from n to closest prime. |
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+0
15
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| 2, 1, 0, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1
(list; graph; listen)
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OFFSET
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0,1
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
Eric Weisstein's World of Mathematics, Prime Distance
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FORMULA
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Conjecture: S(n) = sum(k=1, n, a(k) ) is asymptotic to C*n*log(n) with C=0.29...... - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 11 2002
Comment from Giorgio Balzarotti (greenblue(AT)tiscali.it), Sep 18 2005: by means of the Prime Number Theorem is possible to derive the following inequality : c1*n*log(n) < S(n)< c2*n*log(n), where log is the natural logarithm, and c1 = 1/4 and c2 = 3/8 (for n > 130). For a more accurate estimation of the values for c1 and c2, it necessary to know the number of twin primes with respect to the total number of primes.
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EXAMPLE
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Closest primes to 0,1,2,3,4 are 2,2,2,3,3.
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MATHEMATICA
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FormatSequence[ Table[Min[Abs[n-If[n<2, 2, Prime[{#, #+1}&[PrimePi[n]]]]]], {n, 0, 101}], 51699, 0, Name->"Distance to closest prime." ]
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PROGRAM
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(PARI) a(n)=if(n<1, 2*(n==0), vecmin(vector(n, k, abs(n-prime(k)))))
(PARI) a(n)=if(n<1, 2*(n==0), min(nextprime(n)-n, n-precprime(n)))
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CROSSREFS
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Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.
Adjacent sequences: A051696 A051697 A051698 this_sequence A051700 A051701 A051702
Sequence in context: A140727 A140728 A130068 this_sequence A007920 A127587 A082926
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu)
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