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 A051699 Distance from n to closest prime. 22
 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; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Prime Distance FORMULA Conjecture: S(n) = sum(k=1, n, a(k) ) is asymptotic to C*n*log(n) with C=0.29...... - Benoit Cloitre, Aug 11 2002 Comment from Giorgio Balzarotti, 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. EXAMPLE Closest primes to 0,1,2,3,4 are 2,2,2,3,3. MAPLE A051699 := proc(n) if isprime(n) then 0; elif n<= 2 then 2-n ; else min(nextprime(n)-n, n-prevprime(n)) ; end if ; end proc; # R. J. Mathar, Nov 01 2009 MATHEMATICA FormatSequence[ Table[Min[Abs[n-If[n<2, 2, Prime[{#, #+1}&[PrimePi[n]]]]]], {n, 0, 101}], 51699, 0, Name->"Distance to closest prime." ] (* From version 6 on: *) a[_?PrimeQ] = 0; a[n_] := Min[NextPrime[n]-n, n-NextPrime[n, -1]]; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Apr 05 2012 *) PROG (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))) CROSSREFS Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730. Sequence in context: A130068 A316825 A246398 * A007920 A127587 A175832 Adjacent sequences:  A051696 A051697 A051698 * A051700 A051701 A051702 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from James A. Sellers STATUS approved

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Last modified July 17 14:44 EDT 2019. Contains 325106 sequences. (Running on oeis4.)