A086517 a(1) = 1 and then the smallest odd number not included earlier such that the arithmetic mean of a pair of successive terms is prime.

1, 3, 7, 15, 11, 23, 35, 27, 19, 39, 43, 31, 51, 55, 63, 59, 47, 71, 75, 67, 79, 87, 91, 103, 99, 95, 83, 111, 107, 119, 135, 127, 147, 115, 139, 123, 131, 143, 155, 159, 167, 179, 183, 151, 163, 171, 175, 187, 195, 191, 203, 219, 227, 231, 215, 207, 239, 243, 211

Offset: 1

Author

Amarnath Murthy, Jul 30 2003

Keywords

• nonn

Comments

Second term onwards rearrangement of odd numbers of the type 4n+3.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A086518.

Cf. A259565, A259260, A259429, A259542, A010051, A005408.

Programs

Haskell

import Data.List (delete)
a086517 n = a086517_list !! (n-1)
a086517_list = 1 : f 1 [3, 5 ..] where
   f x zs = g zs where
     g (y:ys) = if a010051' ((x + y) `div` 2) == 1
                   then y : f y (delete y zs) else g ys
-- Reinhard Zumkeller, Jun 30 2015

PARI

v=[1];n=1;while(n<100,s=(n+v[#v])/2;if(type(s)=="t_INT",if(isprime(s)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=0));n++);v \\ Derek Orr, Jun 16 2015

Extensions

More terms from David Wasserman, Mar 10 2005