A374507 Prime numbers that precede and follow consecutive balanced primes.

7829, 32491, 40087, 40099, 50423, 104009, 128461, 166967, 167747, 169307, 186259, 203011, 206209, 245759, 253987, 260387, 267581, 295271, 297403, 311021, 331159, 336163, 353081, 370009, 381389, 396079, 396449, 442843, 455431, 481513, 577867, 596599, 605861

Offset: 1

Author

Kishin Ikemoto, Jul 09 2024

Keywords

• nonn

Examples

			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.
		

Links

• Kishin Ikemoto, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006562 (balanced primes).

Programs

C

#include 
#define K 5
#include 
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;
}

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 *)