login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A075893 Average of three successive primes squared, (prime(n)^2+prime(n+1)^2+prime(n+2)^2)/3, n>=3. 4
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; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

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, Sep 30 2007

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 3..5000

FORMULA

a(n) = (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, Sep 30 2007 *)

Mean[#]&/@Partition[Prime[Range[3, 50]]^2, 3, 1] (* Harvey P. Dale, Jun 09 2013 *)

PROG

(MAGMA) [(NthPrime(n)^2+NthPrime(n+1)^2+NthPrime(n+2)^2)/3: n in [3..50]]; // Vincenzo Librandi, Aug 21 2018

CROSSREFS

Cf. A133529, A084951, A133940.

Sequence in context: A063519 A299456 A300094 * A064901 A039482 A247676

Adjacent sequences:  A075890 A075891 A075892 * A075894 A075895 A075896

KEYWORD

easy,nonn

AUTHOR

Zak Seidov, Oct 17 2002

EXTENSIONS

Edited by N. J. A. Sloane, Jun 30 2008 at the suggestion of R. J. Mathar

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)