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A340060 Averages k of twin primes such that the sum (with multiplicity) of prime factors of k-1, k and k+1 is prime.

%I A340060 #11 Feb 06 2021 21:52:40
%S A340060 6,12,108,420,432,462,1020,1290,1302,1428,1482,2088,3120,3468,3540,
%T A340060 4092,4242,5280,5652,5850,5868,6690,7332,8820,9420,9462,9930,10038,
%U A340060 10092,11118,11832,11940,14628,16140,16362,17208,17388,17682,18042,18312,20640,20772,22278,22962,23028,23202,25848
%N A340060 Averages k of twin primes such that the sum (with multiplicity) of prime factors of k-1, k and k+1 is prime.
%H A340060 Robert Israel, <a href="/A340060/b340060.txt">Table of n, a(n) for n = 1..10000</a>
%e A340060 a(3)=108 is a term because 107 and 109 are primes and the sum of prime factors of 107, 108=2^2*3^3 and 109 is 107+2+2+3+3+3+109 = 229, which is prime.
%p A340060 P:= select(isprime, {seq(i,i=3..10^6,2)}):
%p A340060 T:= map(`+`,P,1) intersect map(`-`,P,1):
%p A340060 filter:= proc(t) local s; isprime(2*t+add(s[1]*s[2],s=ifactors(t)[2])) end proc:
%p A340060 sort(convert(select(filter,T),list));
%Y A340060 Subset of A014574. Cf. A001414, A046363.
%Y A340060 a(n) = A330488(n)+1.
%K A340060 nonn
%O A340060 1,1
%A A340060 _J. M. Bergot_ and _Robert Israel_, Dec 27 2020