OFFSET
1,1
LINKS
Kishin Ikemoto, Table of n, a(n) for n = 1..10000
EXAMPLE
7817, 7823, 7829, 7841, and 7853 are consecutive primes. Since 7823 and 7841 are consecutive balanced primes (7817 + 7829 = 2*7823, 7829 + 7853 = 2*7841), 7829 is in this sequence.
MAPLE
p, q, r, s, t:= 2, 3, 5, 7, 11:
count:= 0: R:= NULL:
while count < 40 do
p, q, r, s:= q, r, s, t;
t:= nextprime(t);
if p+r = 2*q and r+t = 2*s then
count:= count+1;
R:= R, r;
fi;
od:
R; # Robert Israel, Jul 11 2024
MATHEMATICA
Select[Partition[Prime[Range[50000]], 5, 1], #[[2]]==(#[[1]]+#[[3]])/2&&#[[4]]==(#[[3]]+#[[5]])/2&][[;; , 3]] (* Harvey P. Dale, Sep 17 2024 *)
PROG
(C)
#include <stdio.h>
#define K 5
#include <math.h>
int main(void) {
int x[K], primej, z, md, n, maxd, count;
x[0] = 2; x[1] = 3; x[2] = 5; x[3] = 7; x[4] = 11;
primej = 1;
n = 13;
maxd = 3;
count = 0;
while (count < 50) {
for (md = 2; md <= maxd; md++) {
if (n % md == 0) {
primej = 0;
}
}
if (primej == 1) {
x[0] = x[1]; x[1] = x[2]; x[2] = x[3]; x[3] = x[4]; x[4] = n;
if (x[0] + x[2] == 2 * x[1] && x[2] + x[4] == 2 * x[3]) {
z = x[2];
count++;
printf("%d %d\n", count, z);
}
}
n += 2;
maxd = sqrt((double)n);
primej = 1;
}
return 0;
}
CROSSREFS
KEYWORD
nonn
AUTHOR
Kishin Ikemoto, Jul 09 2024
STATUS
approved