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a(n) = (prime(prime(2*n)) - prime(2*prime(n)))/2.
2

%I #17 Nov 04 2024 01:32:41

%S -1,2,6,12,15,28,26,39,42,41,54,44,63,72,63,81,75,102,105,105,124,121,

%T 117,174,133,134,160,181,190,197,152,198,170,240,189,210,233,243,238,

%U 232,249,289,238,283,296,339,300,228,262,330,357,371,384,378,372

%N a(n) = (prime(prime(2*n)) - prime(2*prime(n)))/2.

%C As difference of two odd primes, all terms of A230481(n) = prime(prime(2*n))-prime(2*prime(n)) are even, which motivates to define the present sequence.

%C Further values: a(100)=617, a(10^3)=9344, a(10^4)=114171, a(10^5)=1325772, a(10^6)=14979156; a(10^10)~2.2*10^11, a(10^20)~3.9*10^21, a(10^30)~5.5*10^31.

%H M. F. Hasler, <a href="/A230482/b230482.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (A217622(n) - A230460(n))/2.

%o (PARI) a=n->(prime(prime(2*n))-prime(2*prime(n)))/2

%Y Cf. A066066, A000040, A006450, A031215, A217622, A230460.

%K sign

%O 1,2

%A _M. F. Hasler_, Oct 20 2013