A024697 a(n) = p(1)p(n) + p(2)p(n-1) + ... + p(k)p(n+1-k), where k = [ (n+1)/2 ], p = A000040 = the primes.

4, 6, 19, 29, 68, 94, 177, 231, 400, 484, 753, 903, 1340, 1552, 2157, 2489, 3352, 3784, 5013, 5515, 7052, 7758, 9773, 10575, 13076, 14076, 17023, 18339, 21876, 23414, 27715, 29437, 34570, 36500, 42335, 44731, 51560, 54198, 61955, 65051, 73700, 77402, 87293

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

a(n) = A025129(n) for even n. - M. F. Hasler, Apr 06 2014

Links

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

Crossrefs

Cf. A014342, A000040.

Programs

Haskell

a024697 n = a024697_list !! (n-1)
a024697_list = f (tail a000040_list) [head a000040_list] 2 where
   f (p:ps) qs k = sum (take (div k 2) $ zipWith (*) qs $ reverse qs) :
                   f ps (p : qs) (k + 1)
-- Reinhard Zumkeller, Apr 07 2014

Maple

A024697:=n->sum( ithprime(k)*ithprime(n-k+1), k=1..(n+1)/2 ); seq(A024697(n), n=1..50); # Wesley Ivan Hurt, Apr 06 2014

Mathematica

Table[Sum[Prime[k] Prime[n - k + 1], {k, (n + 1)/2}], {n, 50}] (* Wesley Ivan Hurt, Apr 06 2014 *)

PARI

A024697(n)=sum(k=1, (n+1)\2, prime(k)*prime(n-k+1)) \\ M. F. Hasler, Apr 06 2014

Extensions

Name edited and values double-checked by M. F. Hasler, Apr 06 2014