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%I #42 Apr 04 2020 17:14:08
%S 0,1,2,4,4,4,4,4,8,6,6,8,4,4,8,10,6,6,8,4,6,8,8,12,10,4,4,4,4,16,16,8,
%T 6,10,10,6,10,8,8,10,6,10,10,4,4,12,22,14,4,4,8,6,10,14,10,10,6,6,8,4,
%U 10,22,16,4,4,16,18,14,10,4,8,12,12,10,8,8,12
%N Numbers of previous and following composites of n-th prime.
%C Essentially the same as A046930. - _R. J. Mathar_, Apr 16 2009
%C For twin primes this is the gap before or after the twins, e.g., a(17) = 6 = 59 - 53 = prime(17) - prime(16) for the twin (59, 61) with a(18) = 6 = 67 - 61 = prime(19) - prime(18). - _Frank Ellermann_, Mar 17 2020
%H Harvey P. Dale, <a href="/A159461/b159461.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Pri#gaps">Index entries for gaps between primes</a>.
%F For n >= 2, we have
%F a(n) = A001223(n) + A001223(n-1) - 2;
%F a(n) = A046933(n) + A046933(n-1);
%F a(n) = A008578(n+2) - A008578(n) - 2;
%F a(n) = A158611(n+3) - A158611(n+1) - 2.
%e For a(16) = 10 = 59 - 47 - 2 = prime(16+1) - prime(16-1) - 2 is the sum of the prime gaps minus two ending and starting at prime(16) = 53.
%t Join[{0},Total[Differences[#]-1]&/@Partition[Prime[Range[60]],3,1]] (* _Harvey P. Dale_, Nov 27 2011 *)
%Y Cf. A000040, A001223, A046933, A008578, A158611.
%K nonn
%O 1,3
%A _Jaroslav Krizek_, Apr 12 2009
%E Correction for change of offset in A158611 and A008578 in Aug 2009 _Jaroslav Krizek_, Jan 27 2010
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