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

Author

Jon Perry, Jun 23 2003

Keywords

• nonn

Examples

			a(4) = 11*3 + 7*5 + 5*7 + 3*11 = 136.
		

Links

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

Crossrefs

Cf. A065091, A014342, A209403.

Programs

Mathematica

Table[With[{c=Prime[Range[2,n]]},ListConvolve[c,c]],{n,2,40}]//Flatten (* Harvey P. Dale, Apr 25 2016 *)

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

Formula

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