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

1,1

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).

Links

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

Example

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

Mathematica

Select[Range@ 162, # > (Abs@ 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, A264720, A264721, A264722.

Sequence in context: A274564 A373664 A112787 * A214792 A214897 A037307

Adjacent sequences: A264716 A264717 A264718 * A264720 A264721 A264722

Keyword

nonn,easy

Author

Chris Boyd, Nov 21 2015

Status

approved