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%I #19 Sep 08 2022 08:45:07
%S 65,113,193,273,393,577,777,1057,1337,1633,1913,2289,2833,3337,3897,
%T 4417,4953,5537,6153,7017,8073,9177,10073,10753,11313,12033,13593,
%U 15353,17353,18417,20097,21441,23217,24673,26369,28129,29953,31577,33761
%N Average of three successive primes squared, (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3.
%C Unlike the average of three successive primes, the average of three successive primes (greater than 3) squared is always integral.
%C A133529(n)/3, n >= 3. - _Artur Jasinski_, Sep 30 2007
%H Vincenzo Librandi, <a href="/A075893/b075893.txt">Table of n, a(n) for n = 3..5000</a>
%F a(n) = (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3.
%e a(3)=65 because (prime(3)^2+prime(4)^2+prime(5)^2)/3=(5^2+7^2+11^2)/3=65.
%t b = {}; a = 2; Do[k = (Prime[n]^a + Prime[n + 1]^a + Prime[n + 2]^a)/3; AppendTo[b, k], {n, 3, 50}]; b (* _Artur Jasinski_, Sep 30 2007 *)
%t Mean[#]&/@Partition[Prime[Range[3,50]]^2,3,1] (* _Harvey P. Dale_, Jun 09 2013 *)
%o (Magma) [(NthPrime(n)^2+NthPrime(n+1)^2+NthPrime(n+2)^2)/3: n in [3..50]]; // _Vincenzo Librandi_, Aug 21 2018
%Y Cf. A133529, A084951, A133940.
%K easy,nonn
%O 3,1
%A _Zak Seidov_, Oct 17 2002
%E Edited by _N. J. A. Sloane_, Jun 30 2008 at the suggestion of _R. J. Mathar_
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