A084370 Convolution of odd primes with themselves.

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

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A065091, A014342, A209403.

Sequence in context: A073399 A225275 A005919 * A000439 A002414 A273604

Adjacent sequences: A084367 A084368 A084369 * A084371 A084372 A084373

Keyword

nonn

Author

Jon Perry, Jun 23 2003

Status

approved