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A226152
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Numbers n such that n^2 is an average of 4 consecutive primes.
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0
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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MAPLE
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add(ithprime(i), i=n..n+3) ;
end proc:
for n from 1 to 90000 do
if type(s, 'integer') then
if issqr(s) then
printf("%d, ", sqrt(s)) ;
end if;
end if;
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PROG
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(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;
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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