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Numbers that are greater than the average of their closest flanking primes.
+10
4
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
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.
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, ", ")))
Numbers that are less than the average of their closest flanking primes.
+10
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
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.
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, ", ")))
Composite numbers that are greater than the average of their closest flanking primes.
+10
4
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
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.
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, ", ")))
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