The On-Line Encyclopedia of Integer Sequences (OEIS)

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A214451

Arithmetic mean of next a(n) successive squares of positive integers is prime.
(history; published version)

#8 by Susanna Cuyler at Wed May 02 22:35:43 EDT 2018

STATUS

proposed

approved

#7 by Robert Israel at Wed May 02 16:23:03 EDT 2018

STATUS

editing

proposed

#6 by Robert Israel at Wed May 02 16:22:54 EDT 2018

COMMENTS

All terms are in A007310. Do all members of A007310 except 1 occur? - Robert Israel, May 02 2018

LINKS

Robert Israel, <a href="/A214451/b214451.txt">Table of n, a(n) for n = 1..10000</a>

MAPLE

r:= 0:

for n from 1 to 100 do

t:= 0:

for j from r+1 do

t:= t + j^2;

s:= t/(j-r);

if s::integer and isprime(s) then

A[n]:= j-r;

r:= j;

break

fi

od;

od:

seq(A[i], i=1..100); # Robert Israel, May 02 2018

CROSSREFS

Cf. A000040, A000290, A007310, A214442, A214444.

STATUS

approved

editing

#5 by N. J. A. Sloane at Sun Jul 22 17:19:43 EDT 2012

STATUS

proposed

approved

#4 by Alex Ratushnyak at Wed Jul 18 13:28:23 EDT 2012

STATUS

editing

proposed

#3 by Alex Ratushnyak at Wed Jul 18 13:27:10 EDT 2012

COMMENTS

Corresponding primes (arithmetic means) :

11, 131, 1031, 4643, 9433, 30671, 59063, 64013, 70249, 76733, 94483, 117679, 133277, 156127, 198377, 257339, 297049, 326143, 417089, 522883, 573101, 619471, 651251, 660973, 670763

EXAMPLE

(1+4+9+16+25)/5 = 11, so a(1)=5. The next set of successive squares with prime arithmetic mean: (6^2 + 7^2 + ... + 16^2)/11=131, so a(2)=11.

#2 by Alex Ratushnyak at Wed Jul 18 13:05:44 EDT 2012

NAME

allocated for Alex RatushnyakArithmetic mean of next a(n) successive squares of positive integers is prime.

DATA

5, 11, 29, 43, 17, 131, 13, 7, 17, 7, 53, 19, 25, 35, 65, 59, 17, 35, 113, 43, 25, 35, 5, 7, 5, 11, 89, 23, 17, 35, 29, 43, 5, 31, 109, 71, 65, 7, 41, 31, 61, 35, 25, 107, 25, 11, 41, 47, 25, 175, 41, 35, 29, 23, 17, 43, 197, 91, 13, 95, 17, 47, 5, 7, 25, 11

OFFSET

1,1

CROSSREFS

Cf. A000040, A000290, A214442, A214444.

KEYWORD

allocated

nonn

AUTHOR

Alex Ratushnyak, Jul 18 2012

STATUS

approved

editing

#1 by Alex Ratushnyak at Wed Jul 18 13:05:44 EDT 2012

NAME

allocated for Alex Ratushnyak

KEYWORD

allocated

STATUS

approved