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

6, 12, 108, 420, 432, 462, 1020, 1290, 1302, 1428, 1482, 2088, 3120, 3468, 3540, 4092, 4242, 5280, 5652, 5850, 5868, 6690, 7332, 8820, 9420, 9462, 9930, 10038, 10092, 11118, 11832, 11940, 14628, 16140, 16362, 17208, 17388, 17682, 18042, 18312, 20640, 20772, 22278, 22962, 23028, 23202, 25848

Offset: 1

Author

J. M. Bergot and Robert Israel, Dec 27 2020

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Subset of A014574. Cf. A001414, A046363.

a(n) = A330488(n)+1.

Programs

Maple

P:= select(isprime, {seq(i,i=3..10^6,2)}):
T:= map(`+`,P,1) intersect map(`-`,P,1):
filter:= proc(t) local s; isprime(2*t+add(s[1]*s[2],s=ifactors(t)[2])) end proc:
sort(convert(select(filter,T),list));