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A069495
Squares which are the arithmetic mean of two consecutive primes.
12
4, 9, 64, 81, 144, 225, 324, 441, 625, 1089, 1681, 2601, 3600, 4096, 5184, 6084, 8464, 12544, 13689, 16641, 19044, 19600, 25281, 27225, 28224, 29584, 36864, 38025, 39204, 45369, 46656, 47524, 51984, 56169, 74529, 87025, 88804, 91809, 92416, 95481, 103684
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
Intersection of A000290 and A024675.
Sequence in context: A380949 A028822 A270696 * A029788 A062826 A201918
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Mar 30 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Apr 01 2002
STATUS
approved