A264720 Numbers that are less than the average of their closest flanking primes.

3, 7, 8, 13, 14, 19, 20, 23, 24, 25, 31, 32, 33, 38, 43, 44, 47, 48, 49, 54, 55, 61, 62, 63, 68, 73, 74, 75, 80, 83, 84, 85, 89, 90, 91, 92, 98, 103, 104, 109, 110, 113, 114, 115, 116, 117, 118, 119, 128, 131, 132, 133, 139, 140, 141, 142, 143, 151, 152, 153, 158

Offset: 1

Author

Chris Boyd, Nov 21 2015

Keywords

• nonn
• easy

Comments

Numbers that are nearer to the immediately previous prime than to the immediately next prime.

This sequence may be viewed as a generalization of A051635 (the weak primes) that includes qualifying composite numbers.

The union of this sequence with A264719 & A145025 is A000027 (omitting 1 & 2).

Examples

			a(11) = 31 because 31 < (29 + 37)/2 = 33.
a(12) = 32 because 32 < (31 + 37)/2 = 34.
		

Links

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

Crossrefs

Cf. A051634, A145025, A264719, A264721, A264722.

Programs

Mathematica

Select[Range@ 162, # < (NextPrime[#, -1] + NextPrime@ #)/2 &] (* Michael De Vlieger, Nov 22 2015 *)

PARI

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