A109269 Numbers n such that n^2 < (1/2)*(prevprime(n^2)+nextprime(n^2)).
5, 7, 13, 19, 23, 27, 29, 32, 34, 35, 37, 42, 43, 44, 46, 47, 49, 53, 55, 58, 61, 63, 68, 69, 71, 75, 77, 80, 82, 83, 86, 88, 89, 93, 98, 101, 102, 103, 107, 108, 113, 118, 119, 121, 127, 128, 131, 132, 133, 135, 136, 139, 142, 143, 144, 145, 149, 152, 155, 161, 164
Offset: 1
Keywords
Examples
7 is in the sequence because 49 is less than (47+53)/2=50, 8 is not in the sequence because 64=(61+67)/2.
Programs
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Maple
a:=proc(n) if n^2< (1/2)*(prevprime(n^2)+nextprime(n^2)) then n else fi end: seq(a(n),n=2..200); # Emeric Deutsch, Jun 26 2005
Extensions
More terms from Emeric Deutsch, Jun 26 2005