A261543 - OEIS

%I #16 Feb 16 2025 08:33:26

%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="https://mathworld.wolfram.com/PrimeNumber.html">Prime Number </a>

%H Eric Weisstein's World of Mathematics, <a href="https://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,changed

%O 1,1

%A _Ilya Gutkovskiy_, Aug 24 2015