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A084370 Convolution of odd primes with themselves. 1
9, 30, 67, 136, 237, 386, 587, 852, 1213, 1658, 2227, 2932, 3765, 4766, 5939, 7324, 8917, 10746, 12851, 15200, 17845, 20794, 24083, 27748, 31785, 36250, 41107, 46376, 52113, 58350, 65111, 72444, 80353, 88858, 98003, 107744, 118201, 129410, 141355, 154080 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) = Sum_{k=1..n} A065091(k) * A065091(n-k+1).
EXAMPLE
a(4) = 11*3 + 7*5 + 5*7 + 3*11 = 136.
MATHEMATICA
Table[With[{c=Prime[Range[2, n]]}, ListConvolve[c, c]], {n, 2, 40}]//Flatten (* Harvey P. Dale, Apr 25 2016 *)
PROG
(PARI) conv(n)=local(v, s); v=primes(n+1); s=0; for(i=2, length(v), s+=v[i]*v[length(v)-i+2]); s
for(n=1, 40, print1(conv(n)", "))
(Python)
from numpy import convolve
from sympy import prime, primerange
def aupton(terms):
p = list(primerange(3, prime(terms+1)+1))
return list(convolve(p, p))[:terms]
print(aupton(40)) # Michael S. Branicky, Sep 30 2021
CROSSREFS
Sequence in context: A073399 A225275 A005919 * A000439 A002414 A273604
KEYWORD
nonn
AUTHOR
Jon Perry, Jun 23 2003
STATUS
approved

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Last modified March 4 02:53 EST 2024. Contains 370522 sequences. (Running on oeis4.)