A209403 Convolution of primes with odd primes.

6, 19, 44, 89, 162, 271, 424, 633, 910, 1275, 1732, 2309, 3018, 3859, 4872, 6057, 7446, 9051, 10888, 12997, 15358, 18011, 20972, 24277, 27950, 31991, 36464, 41325, 46602, 52367, 58612, 65385, 72722, 80651, 89160, 98317, 108070, 118535, 129756, 141713, 154442

Offset: 1

Author

Reinhard Zumkeller, Mar 08 2012

Keywords

• nonn

Examples

			a(2) = 2*5 + 3*3 = 19.
		

Links

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

Crossrefs

Cf. A000040, A065091, A014342.

Programs

Haskell

a209403 n = sum $
   zipWith (*) (reverse $ take n a000040_list) a065091_list

Magma

[&+[NthPrime(k)*NthPrime(n+1-k): k in [1..n-1]]: n in [2..40]]; // Bruno Berselli, Mar 08 2012

Mathematica

Rest[Flatten[Table[ListConvolve[Prime[Range[2,n]],Prime[Range[n-1]]],{n,50}]]] (* Harvey P. Dale, Jan 10 2022 *)

Python

from numpy import convolve
from sympy import prime, primerange
def aupton(nn):
    primes = list(primerange(2, prime(nn+1)+1))
    return list(convolve(primes[:-1], primes[1:]))[:nn]
print(aupton(41)) # Michael S. Branicky, Jun 19 2021

Formula

a(n) = Sum_{k=1..n} A000040(k) * A065091(n-k+1).