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%I #15 Sep 18 2015 11:34:30
%S 2,5,8,15,20,42,60,137,210,520,828,2124,3418,8895,14370,37561,60747,
%T 158959,257169,673198,1089220,2851513,4613807,12078987,19544166,
%U 51167164,82790160,216747314,350704463,918156051,1485607642,3889371138,6293134627
%N Numbers of the form (prime(k) + Fibonacci(k))/2.
%C The numbers represented as the arithmetic mean of the Fibonacci numbers and prime numbers with identical indices.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeNumber.html">Prime Number </a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciNumber.html">Fibonacci Number </a>
%F a(n) = (prime(A001651(n + 1)) + Fibonacci(A001651(n + 1)))/2
%e a(1) = (prime(2) + Fibonacci(2))/2 = (3 + 1)/2 = 2.
%t Select[Array[(Prime[#] + Fibonacci@ #)/2 &, 50], IntegerQ] (* _Michael De Vlieger_, Aug 24 2015 *)
%o (PARI) a(n)=n+=n\2+1; (prime(n)+fibonacci(n))/2 \\ _Charles R Greathouse IV_, Aug 24 2015
%Y Cf. A000040, A000045, A004397, A001651.
%K nonn,easy
%O 1,1
%A _Ilya Gutkovskiy_, Aug 24 2015
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