OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)
FORMULA
a(n) = (A075190(n))^2. - Zak Seidov
EXAMPLE
144 = (139 + 149)/2 is a member.
MAPLE
a:= proc(n) option remember; local k, kk, p, q;
for k from 1 +`if`(n=1, 1, iroot(a(n-1), 2))
do kk:= k^2; p, q:= prevprime(kk), nextprime(kk);
if (p+q)/2=kk then return kk fi
od
end:
seq(a(n), n=1..60); # Alois P. Heinz, Dec 21 2013
MATHEMATICA
p = -1; Do[q = Prime[n]; If[ IntegerQ[ Sqrt[(p + q)/2]], Print[(p + q)/2]]; p = q, {n, 1, 10000} ]
Select[Mean/@Partition[Prime[Range[11000]], 2, 1], IntegerQ[Sqrt[#]]&] (* Harvey P. Dale, Jan 23 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Mar 30 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Apr 01 2002
STATUS
approved