%I #15 Jul 28 2020 17:53:37

%S 8,14,20,24,25,32,33,38,44,48,49,54,55,62,63,68,74,75,80,84,85,90,91,

%T 92,98,104,110,114,115,116,117,118,119,128,132,133,140,141,142,143,

%U 152,153,158,159,164,168,169,174,175,182,183,184,185,194,200,201,202,203

%N Composite numbers that are less than the average of their closest flanking primes.

%C Composite numbers that are nearer to the immediately previous prime than to the immediately next prime.

%C Members of this sequence are the numbers C, necessarily composite, such that P_n < C < I_n, where P_n is the n-th odd prime and I_n the interprime (A024675) between P_n and P_n+1.

%C Prime-free subsequence of A264720.

%H Chris Boyd, <a href="/A264722/b264722.txt">Table of n, a(n) for n = 1..10000</a>

%e a(7) = 33 because 33 < (31 + 37)/2 = 34.

%t Select[Range@ 204, And[CompositeQ@ #, # < (NextPrime[#, -1] + NextPrime@ #)/2] &] (* _Michael De Vlieger_, Nov 22 2015 *)

%t Range[#[[1]]+1,Total[#]/2 -1]&/@Select[Partition[Prime[Range[50]],2,1], #[[2]]- #[[1]]>2&]//Flatten (* _Harvey P. Dale_, Jul 28 2020 *)

%o (PARI) test(n)= {if(n-precprime(n-1)<nextprime(n+1)-n&&n>2&&!isprime(n),return(1),return(0))}

%o for(i=1,200,if(test(i),print1(i,", ")))

%Y Cf. A264719, A264720, A264721.

%K nonn,easy

%O 1,1

%A _Chris Boyd_, Nov 21 2015