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

1,1

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.

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A264719, A264720, A264721.

Sequence in context: A078754 A068638 A025044 * A125163 A309355 A063288

Adjacent sequences: A264719 A264720 A264721 * A264723 A264724 A264725

Keyword

nonn,easy

Author

Chris Boyd, Nov 21 2015

Status

approved