%I #24 Nov 07 2023 08:22:42

%S 2,7,9,15,15,21,21,27,35,33,43,45,45,51,59,65,63,73,75,75,85,87,95,

%T 105,105,105,111,111,117,141,135,143,141,159,153,163,169,171,179,185,

%U 183,201,195,201,201,223,235,231,231,237,245,243,261,263,269,275,273,283,285,285,303,321,315,315,321,345,343,357,351,357,365,375,379

%N Numerator of prime(n+1) - prime(n)/2.

%C Second row of the inverse semi-binomial transform of A000040(n+1) as introduced in A213268.

%C The list of denominators is 1, 2, 2, ... (2 repeated), so a(n) = A210497(n) for n>1.

%C a(n) - prime(n) = 2*prime(n+1)-prime(n)-prime(n) are prime differences (A001223) multiplied by 2, and therefore multiples of 4.

%F a(n) ~ n log n. Apart from the first term, a(n) = 2*prime(n+1) - prime(n). - _Charles R Greathouse IV_, Jul 10 2012

%F a(n) = prime(n+2) - A036263(n), n>1. - _R. J. Mathar_, Jul 10 2012

%p A211280 := proc(n)

%p ithprime(n+1)-ithprime(n)/2 ;

%p numer(%) ;

%p end proc: # _R. J. Mathar_, Jul 10 2012

%t Numerator[#[[2]]-#[[1]]/2]&/@Partition[Prime[Range[80]],2,1] (* _Harvey P. Dale_, Mar 05 2023 *)

%Y Denominators are A040000.

%K nonn,easy,frac

%O 1,1

%A _Paul Curtz_, Jul 05 2012