A264721 Composite numbers that are greater than the average of their closest flanking primes.

10, 16, 22, 27, 28, 35, 36, 40, 46, 51, 52, 57, 58, 65, 66, 70, 77, 78, 82, 87, 88, 94, 95, 96, 100, 106, 112, 121, 122, 123, 124, 125, 126, 130, 135, 136, 145, 146, 147, 148, 155, 156, 161, 162, 166, 171, 172, 177, 178, 187, 188, 189, 190, 196, 206, 207, 208

Offset

1,1

Comments

Composite numbers that are nearer to the immediately next prime than to the immediately previous prime.

Members of this sequence are the numbers C, necessarily composite, such that I_n < C < P_n+1, 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 A264719.

Links

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

Example

a(7) = 36 because 36 > (31 + 37)/2 = 34.

Mathematica

Select[Range@ 208, And[CompositeQ@ #, # > (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&&!isprime(n), return(1), return(0))}
for(i=1, 200, if(test(i), print1(i, ", ")))

Crossrefs

Cf. A264719, A264720, A264722.

Sequence in context: A238204 A242057 A245024 * A136799 A055987 A187397

Adjacent sequences: A264718 A264719 A264720 * A264722 A264723 A264724

Keyword

nonn,easy

Author

Chris Boyd, Nov 21 2015

Status

approved