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a(n) is the integer-valued average gap between successive primes from prime(1) to prime(k(n)), where k(n) = A049036(n).
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%I #9 Aug 25 2013 15:39:50

%S 1,3,5,7,7,9,13,13,13,15,15,19,19,19,19,19,21,21,27,29,31

%N a(n) is the integer-valued average gap between successive primes from prime(1) to prime(k(n)), where k(n) = A049036(n).

%C a(n) arises from A049036 and A049038.

%F a(n) = (A049038(n)-2)/(A049036(n)-1).

%e For n=1 a(n)=(p(k(1))-2)/(k(1)-1), where k(1)=2, p(2)=3, and a(1)=1;

%e For n=2 a(n)=(p(k(2))-2)/(k(2)-1), where k(2)=10, p(10)=29, and a(2)=3;

%e For n=3 a(n)=(p(k(3))-2)/(k(3)-1), where k(3)=68, p(68)=337, and a(3)=5;

%t a = {}; Do[s = (Prime[k] - 2)/(k - 1); If[IntegerQ[s], AppendTo[a, s]], {k, 2, 1000000000}]; a

%Y Cf. A049036, A049038.

%K nonn,more

%O 1,2

%A _V.J. Pohjola_, Aug 25 2013