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

1,1

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

Cf. A006562 (balanced primes).

Sequence in context: A252317 A250026 A374576 * A194352 A234477 A286181

Adjacent sequences: A374504 A374505 A374506 * A374508 A374509 A374510

Keyword

nonn

Author

Kishin Ikemoto, Jul 09 2024

Status

approved