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

%I A349981 #49 Feb 07 2022 08:16:26
%S A349981 6,30,462,1062,1290,1482,1878,2088,2790,3558,4272,4338,6552,6660,7308,
%T A349981 8010,8598,8820,10038,10428,10530,10890,11940,12042,12918,13338,13758,
%U A349981 16980,17418,17580,18252,19992,21588,22038,22740,23742,25848,26862,27738,32028,33288,35730,37548,37782,42180,42570
%N A349981 Midpoints k of a pair of twin primes such that sigma(k) is also the midpoint of a pair of twin primes.
%H A349981 Robert Israel, <a href="/A349981/b349981.txt">Table of n, a(n) for n = 1..10000</a>
%F A349981 a(n) = 6*A202607(n). - _Ivan N. Ianakiev_, Feb 07 2022
%e A349981 a(3) = 462 is a term because sigma(462) = 1152 and 461, 463, 1151 and 1153 are primes.
%p A349981 filter:= proc(x) local t;
%p A349981   if not (isprime(x-1) and isprime(x+1)) then return false fi;
%p A349981   t:= numtheory:-sigma(x);
%p A349981   t mod 6 = 0 and isprime(t-1) and isprime(t+1)
%p A349981 end proc:
%p A349981 select(filter, [seq(i,i=6..100000,6)]);
%Y A349981 Intersection of A014574 and A068017.
%Y A349981 Cf. A000203, A202607.
%K A349981 nonn
%O A349981 1,1
%A A349981 _J. M. Bergot_ and _Robert Israel_, Feb 06 2022