A349981 Midpoints k of a pair of twin primes such that sigma(k) is also the midpoint of a pair of twin primes.

6, 30, 462, 1062, 1290, 1482, 1878, 2088, 2790, 3558, 4272, 4338, 6552, 6660, 7308, 8010, 8598, 8820, 10038, 10428, 10530, 10890, 11940, 12042, 12918, 13338, 13758, 16980, 17418, 17580, 18252, 19992, 21588, 22038, 22740, 23742, 25848, 26862, 27738, 32028, 33288, 35730, 37548, 37782, 42180, 42570

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 06 2022

Keywords

• nonn

Examples

			a(3) = 462 is a term because sigma(462) = 1152 and 461, 463, 1151 and 1153 are primes.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A014574 and A068017.

Cf. A000203, A202607.

Programs

Maple

filter:= proc(x) local t;
  if not (isprime(x-1) and isprime(x+1)) then return false fi;
  t:= numtheory:-sigma(x);
  t mod 6 = 0 and isprime(t-1) and isprime(t+1)
end proc:
select(filter, [seq(i,i=6..100000,6)]);

Formula

a(n) = 6*A202607(n). - Ivan N. Ianakiev, Feb 07 2022