A261543 Numbers of the form (prime(k) + Fibonacci(k))/2.

2, 5, 8, 15, 20, 42, 60, 137, 210, 520, 828, 2124, 3418, 8895, 14370, 37561, 60747, 158959, 257169, 673198, 1089220, 2851513, 4613807, 12078987, 19544166, 51167164, 82790160, 216747314, 350704463, 918156051, 1485607642, 3889371138, 6293134627

Offset: 1

Author

Ilya Gutkovskiy, Aug 24 2015

Keywords

• nonn
• easy

Comments

The numbers represented as the arithmetic mean of the Fibonacci numbers and prime numbers with identical indices.

Examples

			a(1) = (prime(2) + Fibonacci(2))/2 = (3 + 1)/2 = 2.
		

Links

• Eric Weisstein's World of Mathematics, Prime Number
• Eric Weisstein's World of Mathematics, Fibonacci Number

Crossrefs

Cf. A000040, A000045, A004397, A001651.

Programs

Mathematica

Select[Array[(Prime[#] + Fibonacci@ #)/2 &, 50], IntegerQ] (* Michael De Vlieger, Aug 24 2015 *)

PARI

a(n)=n+=n\2+1; (prime(n)+fibonacci(n))/2 \\ Charles R Greathouse IV, Aug 24 2015

Formula

a(n) = (prime(A001651(n + 1)) + Fibonacci(A001651(n + 1)))/2