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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A226152 Numbers n such that n^2 is an average of 4 consecutive primes. 0
3, 9, 12, 21, 24, 35, 72, 126, 129, 179, 189, 194, 198, 214, 243, 253, 255, 279, 304, 322, 432, 443, 480, 487, 511, 523, 663, 681, 696, 699, 711, 717, 721, 734, 738, 796, 802, 838, 910, 975, 1008, 1034, 1070, 1144, 1215, 1230, 1237, 1265, 1276, 1370, 1375, 1386, 1469 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Integers of the form sqrt(A102655(k)) for any k. - R. J. Mathar, Jun 06 2013

LINKS

Table of n, a(n) for n=1..53.

FORMULA

a(n) = A051395(n)/2.

MAPLE

A034963 := proc(n)

    add(ithprime(i), i=n..n+3) ;

end proc:

for n from 1 to 90000 do

    s := A034963(n)/4 ;

    if type(s, 'integer') then

    if issqr(s) then

        printf("%d, ", sqrt(s)) ;

    end if;

    end if;

end do: # R. J. Mathar, Jun 06 2013

PROG

(C)

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

#define TOP (1ULL<<30)

int main() {

  unsigned long long i, j, p1, p2, p3, r, s;

  unsigned char *c = (unsigned char *)malloc(TOP/8);

  memset(c, 0, TOP/8);

  for (i=3; i < TOP; i+=2)

    if ((c[i>>4] & (1<<((i>>1) & 7)))==0 /*&& i<(1ULL<<32)*/)

        for (j=i*i>>1; j<TOP; j+=i)  c[j>>3] |= 1 << (j&7);

  for (p3=2, p2=3, p1=5, i=7; i < TOP; i+=2)

    if ((c[i>>4] & (1<<((i>>1) & 7)))==0) {

      s = p3 + p2 + p1 + i;

      if (s%4==0) {

        s/=4;

        r = sqrt(s);

        if (r*r==s) printf("%llu, ", r);

      }

      p3 = p2, p2 = p1, p1 = i;

    }

  return 0;

}

CROSSREFS

Cf. A102655, A051395, A206280.

Sequence in context: A272027 A310323 A212059 * A155504 A270672 A211217

Adjacent sequences:  A226149 A226150 A226151 * A226153 A226154 A226155

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, May 28 2013

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 September 25 10:58 EDT 2021. Contains 347654 sequences. (Running on oeis4.)