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

1,1

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A000040, A065091, A014342.

Sequence in context: A138357 A299264 A183763 * A272707 A266938 A362602

Adjacent sequences: A209400 A209401 A209402 * A209404 A209405 A209406

Keyword

nonn

Author

Reinhard Zumkeller, Mar 08 2012

Status

approved