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A209403 Convolution of primes with odd primes.

%I A209403 #23 Sep 08 2022 08:46:01
%S A209403 6,19,44,89,162,271,424,633,910,1275,1732,2309,3018,3859,4872,6057,
%T A209403 7446,9051,10888,12997,15358,18011,20972,24277,27950,31991,36464,
%U A209403 41325,46602,52367,58612,65385,72722,80651,89160,98317,108070,118535,129756,141713,154442
%N A209403 Convolution of primes with odd primes.
%H A209403 Reinhard Zumkeller, <a href="/A209403/b209403.txt">Table of n, a(n) for n = 1..10000</a>
%F A209403 a(n) = Sum_{k=1..n} A000040(k) * A065091(n-k+1).
%e A209403 a(2) = 2*5 + 3*3 = 19.
%t A209403 Rest[Flatten[Table[ListConvolve[Prime[Range[2,n]],Prime[Range[n-1]]],{n,50}]]] (* _Harvey P. Dale_, Jan 10 2022 *)
%o A209403 (Haskell)
%o A209403 a209403 n = sum $
%o A209403    zipWith (*) (reverse $ take n a000040_list) a065091_list
%o A209403 (Magma) [&+[NthPrime(k)*NthPrime(n+1-k): k in [1..n-1]]: n in [2..40]]; // _Bruno Berselli_, Mar 08 2012
%o A209403 (Python)
%o A209403 from numpy import convolve
%o A209403 from sympy import prime, primerange
%o A209403 def aupton(nn):
%o A209403     primes = list(primerange(2, prime(nn+1)+1))
%o A209403     return list(convolve(primes[:-1], primes[1:]))[:nn]
%o A209403 print(aupton(41)) # _Michael S. Branicky_, Jun 19 2021
%Y A209403 Cf. A000040, A065091, A014342.
%K A209403 nonn
%O A209403 1,1
%A A209403 _Reinhard Zumkeller_, Mar 08 2012