A264722 Composite numbers that are less than the average of their closest flanking primes.

8, 14, 20, 24, 25, 32, 33, 38, 44, 48, 49, 54, 55, 62, 63, 68, 74, 75, 80, 84, 85, 90, 91, 92, 98, 104, 110, 114, 115, 116, 117, 118, 119, 128, 132, 133, 140, 141, 142, 143, 152, 153, 158, 159, 164, 168, 169, 174, 175, 182, 183, 184, 185, 194, 200, 201, 202, 203

Offset: 1

Author

Chris Boyd, Nov 21 2015

Keywords

• nonn
• easy

Comments

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

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.

Prime-free subsequence of A264720.

Examples

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

Links

• Chris Boyd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A264719, A264720, A264721.

Programs

Mathematica

Select[Range@ 204, And[CompositeQ@ #, # < (NextPrime[#, -1] + NextPrime@ #)/2] &] (* Michael De Vlieger, Nov 22 2015 *)
Range[#[[1]]+1,Total[#]/2 -1]&/@Select[Partition[Prime[Range[50]],2,1], #[[2]]- #[[1]]>2&]//Flatten  (* Harvey P. Dale, Jul 28 2020 *)

PARI

test(n)= {if(n-precprime(n-1)2&&!isprime(n),return(1),return(0))}
for(i=1,200,if(test(i),print1(i,", ")))