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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 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 Cf. A062703. Sequence in context: A217854 A028822 A270696 * A029788 A062826 A201918 Adjacent sequences:  A069492 A069493 A069494 * A069496 A069497 A069498 KEYWORD nonn AUTHOR Amarnath Murthy, Mar 30 2002 EXTENSIONS Edited and extended by Robert G. Wilson v, Apr 01 2002 STATUS approved

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)