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A374507 Prime numbers that precede and follow consecutive balanced primes.

%I A374507 #26 Oct 04 2024 14:20:29
%S A374507 7829,32491,40087,40099,50423,104009,128461,166967,167747,169307,
%T A374507 186259,203011,206209,245759,253987,260387,267581,295271,297403,
%U A374507 311021,331159,336163,353081,370009,381389,396079,396449,442843,455431,481513,577867,596599,605861
%N A374507 Prime numbers that precede and follow consecutive balanced primes.
%H A374507 Kishin Ikemoto, <a href="/A374507/b374507.txt">Table of n, a(n) for n = 1..10000</a>
%e A374507 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.
%p A374507 p,q,r,s,t:= 2,3,5,7,11:
%p A374507 count:= 0: R:= NULL:
%p A374507 while count < 40 do
%p A374507  p,q,r,s:= q,r,s,t;
%p A374507  t:= nextprime(t);
%p A374507  if p+r = 2*q and r+t = 2*s then
%p A374507    count:= count+1;
%p A374507    R:= R,r;
%p A374507  fi;
%p A374507 od:
%p A374507 R; # _Robert Israel_, Jul 11 2024
%t A374507 Select[Partition[Prime[Range[50000]],5,1],#[[2]]==(#[[1]]+#[[3]])/2&&#[[4]]==(#[[3]]+#[[5]])/2&][[;;,3]] (* _Harvey P. Dale_, Sep 17 2024 *)
%o A374507 (C)
%o A374507 #include <stdio.h>
%o A374507 #define K 5
%o A374507 #include <math.h>
%o A374507 int main(void) {
%o A374507     int x[K], primej, z, md, n, maxd, count;
%o A374507     x[0] = 2; x[1] = 3; x[2] = 5; x[3] = 7; x[4] = 11;
%o A374507     primej = 1;
%o A374507     n = 13;
%o A374507     maxd = 3;
%o A374507     count = 0;
%o A374507     while (count < 50) {
%o A374507         for (md = 2; md <= maxd; md++) {
%o A374507             if (n % md == 0) {
%o A374507                 primej = 0;
%o A374507             }
%o A374507         }
%o A374507         if (primej == 1) {
%o A374507             x[0] = x[1]; x[1] = x[2]; x[2] = x[3]; x[3] = x[4]; x[4] = n;
%o A374507             if (x[0] + x[2] == 2 * x[1] && x[2] + x[4] == 2 * x[3]) {
%o A374507                 z = x[2];
%o A374507                 count++;
%o A374507                 printf("%d %d\n", count, z);
%o A374507             }
%o A374507         }
%o A374507         n += 2;
%o A374507         maxd = sqrt((double)n);
%o A374507         primej = 1;
%o A374507     }
%o A374507     return 0;
%o A374507 }
%Y A374507 Cf. A006562 (balanced primes).
%K A374507 nonn
%O A374507 1,1
%A A374507 _Kishin Ikemoto_, Jul 09 2024