login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A075894 Average of four successive primes squared, (prime(n)^2 + prime(n+1)^2 + prime(n+2)^2 + prime(n+3)^2)/4, n>=2. 1
51, 91, 157, 235, 337, 505, 673, 925, 1213, 1465, 1777, 2137, 2587, 3055, 3625, 4183, 4645, 5275, 5875, 6595, 7615, 8605, 9535, 10417, 11035, 11677, 13057, 14485, 16207, 17845, 19363, 20773, 22243, 24055, 25477, 27259, 29107, 30655, 32803 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Unlike the average of four successive primes, the average of four successive primes squared is integer for all n>=2. [corrected by Zak Seidov, Jul 07 2017]

LINKS

Harvey P. Dale, Table of n, a(n) for n = 2..1000

FORMULA

a(n) = (prime(n)^2 + prime(n+1)^2 + prime(n+2)^2 + prime(n+3)^2)/4, n>=2.

EXAMPLE

a(2)=51 because (prime(2)^2 + prime(3)^2 + prime(4)^2 + prime(5)^2)/4 = (3^2 + 5^2 + 7^2 + 11^2)/4 = 51.

MATHEMATICA

Mean[#]&/@(Partition[Prime[Range[2, 50]], 4, 1]^2) (* Harvey P. Dale, Dec 14 2011 *)

Table[(Prime[n]^2 + Prime[n+1]^2 + Prime[n+2]^2 + Prime[n+3]^2)/4, {n, 2, 50}] (* Vincenzo Librandi, Jul 07 2017 *)

PROG

(MAGMA) [(NthPrime(n)^2+NthPrime(n+1)^2+NthPrime(n+2)^2+ NthPrime(n+3)^2)/4: n in [2..50]]; // Vincenzo Librandi, Jul 07 2017

(PARI) a(n, p=prime(n))=my(q=nextprime(p+1), r=nextprime(q+1), s=nextprime(r+1)); norml2([p, q, r, s])/4 \\ Charles R Greathouse IV, Jul 07 2017

(PARI) first(n)=my(p=primes(n+3)); vector(n-1, i, (p[i+1]^2 + p[i+2]^2 + p[i+3]^2 + p[i+4]^2)/4) \\ Charles R Greathouse IV, Jul 07 2017

CROSSREFS

Sequence in context: A253020 A020180 A049328 * A229274 A044140 A044521

Adjacent sequences:  A075891 A075892 A075893 * A075895 A075896 A075897

KEYWORD

easy,nonn

AUTHOR

Zak Seidov, Oct 17 2002

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 December 5 06:52 EST 2021. Contains 349543 sequences. (Running on oeis4.)