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a(n) = (n-th prime > 3) minus (n-th composite number).
3

%I #15 May 20 2021 12:44:53

%S 1,1,3,4,7,7,9,14,15,19,21,22,25,29,34,35,40,43,43,47,50,55,62,65,65,

%T 68,69,71,83,86,91,91,100,101,106,111,113,118,123,124,133,133,135,136,

%U 147,158,161,161,164,169,169,177,182,187,192,193,197,200,201,209,222,225,226

%N a(n) = (n-th prime > 3) minus (n-th composite number).

%H Harvey P. Dale, <a href="/A168563/b168563.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = prime(n+2)-composite(n) = A161671(n+2).

%t Module[{nn=100,pr,cmp},cmp=Select[Range[nn],CompositeQ];pr=Prime[ Range[ 3, Length[cmp]+2]];pr-cmp] (* _Harvey P. Dale_, May 28 2015 *)

%Y Cf. A161671.

%K nonn,easy

%O 1,3

%A _Juri-Stepan Gerasimov_, Nov 29 2009

%E Edited by _Charles R Greathouse IV_, Mar 25 2010