%I #17 Oct 23 2024 01:20:04

%S 114239,144059,933899,1918199,25054499,30495419,33065159,72602039,

%T 255442559,353104079,575473559,808589879,846509819,1042804799,

%U 1055710979,1059728279,1184657879,1247085239,1791627599,2196997739,2323221179,2372469179,2591327159,3063507719,3276652079,4021840859,5489857619,5716553879,6022735799

%N Semiprimes s such that (3s+1)/2 is semiprime and A001414(s)=2*A001414((3s+1)/2).

%C Both a(n) and (3a(n)+1)/2 are odd.

%C Both a(n) and (3a(n)+1)/2 are congruent to 2 mod 3.

%C a(n) is congruent to 3 mod 4.

%C Both a(n) and (3a(n)+1)/2 are congruent to 4 mod 5 and the two prime factors are congruent to 1 and 4 mod 5.

%C Both a(n) and (3a(n)+1)/2 are congruent to 9 mod 10 and the two prime factors are congruent to 1 and 9 mod 10.

%C a(n) is also a solution to the arithmetic differential equation A003415((3m+1)/2)=A003415(m)/2.

%C If a(n) = p*(p-m), with p and p-m prime, then m>=2*sqrt(30p^2+2)-10p.

%C The sum of the reciprocals 1/a(n) converges.

%Y Cf. A001358, A046315, A001414, A003415.

%K nonn

%O 1,1

%A _Zachary P. Bradshaw_, Sep 18 2024

%E One of the editors suggests that the following article is related: https://www.researchgate.net/publication/384084846_A_Family_of_Solutions_to_Arithmetic_Differential_Equations_Involving_the_Collatz_Map - _N. J. A. Sloane_, Oct 23 2024