A264719 Numbers that are greater than the average of their closest flanking primes.

10, 11, 16, 17, 22, 27, 28, 29, 35, 36, 37, 40, 41, 46, 51, 52, 57, 58, 59, 65, 66, 67, 70, 71, 77, 78, 79, 82, 87, 88, 94, 95, 96, 97, 100, 101, 106, 107, 112, 121, 122, 123, 124, 125, 126, 127, 130, 135, 136, 137, 145, 146, 147, 148, 149, 155, 156, 161, 162

Offset: 1

Author

Chris Boyd, Nov 21 2015

Keywords

• nonn
• easy

Comments

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

This sequence may be viewed as a generalization of A051634 (the strong primes) that includes qualifying composite numbers.

The union of this sequence with A264720 & A145025 is A000027 (omitting 1 & 2).

Examples

			a(11) = 37 because 37 > (31 + 41)/2 = 36.
a(12) = 40 because 40 > (37 + 41)/2 = 37.
		

Links

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

Crossrefs

Cf. A051634, A145025, A264720, A264721, A264722.

Programs

Mathematica

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

PARI

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