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A264720
Numbers that are less than the average of their closest flanking primes.
4
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).
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
KEYWORD
nonn,easy
AUTHOR
Chris Boyd, Nov 21 2015
STATUS
approved