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A075893 Average of three successive primes squared, (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3. +0
3
65, 113, 193, 273, 393, 577, 777, 1057, 1337, 1633, 1913, 2289, 2833, 3337, 3897, 4417, 4953, 5537, 6153, 7017, 8073, 9177, 10073, 10753, 11313, 12033, 13593, 15353, 17353, 18417, 20097, 21441, 23217, 24673, 26369, 28129, 29953, 31577, 33761 (list; graph; listen)
OFFSET

3,1

COMMENT

Unlike the average of three successive primes, the average of three successive primes (greater than 3) squared is always integral.

A133529(n)/3, n >= 3. - Artur Jasinski (grafix(AT)csl.pl), Sep 30 2007

FORMULA

(prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3.

EXAMPLE

a(3)=65 because (prime(3)^2+prime(4)^2+prime(5)^2)/3=(5^2+7^2+11^2)/3=65.

MATHEMATICA

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 (grafix(AT)csl.pl), Sep 30 2007

CROSSREFS

Cf. A133529, A084951, A133940.

Sequence in context: A094447 A020224 A063519 this_sequence A064901 A039482 A118159

Adjacent sequences: A075890 A075891 A075892 this_sequence A075894 A075895 A075896

KEYWORD

easy,nonn

AUTHOR

Zak Seidov (zakseidov(AT)yahoo.com), Oct 17 2002

EXTENSIONS

Edited by njas, Jun 30 2008 at the suggestion of R. J. Mathar

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.


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