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

1,1

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).

Links

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

Example

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

Mathematica

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

Prog

(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, ", ")))

Crossrefs

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

Sequence in context: A063657 A108575 A153219 * A215034 A050014 A132017

Adjacent sequences: A264717 A264718 A264719 * A264721 A264722 A264723

Keyword

nonn,easy

Author

Chris Boyd, Nov 21 2015

Status

approved