|
|
A209403
|
|
Convolution of primes with odd primes.
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
|
|
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]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|