A264721 - OEIS

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

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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.