A355591 a(n) = (product of the first n odd primes) - (sum of the first n odd primes).

1, 0, 7, 90, 1129, 14976, 255199, 4849770, 111546337, 3234846488, 100280244907, 3710369067210, 152125131763369, 6541380665834736, 307444891294245379, 16294579238595021986, 961380175077106319097, 58644190679703485491136, 3929160775540133527938979

Offset

0,3

Comments

The parity of a(n) is the opposite of the parity of n.

Links

Robert Israel, Table of n, a(n) for n = 0..348

Formula

a(n) = A070826(n+1) - A071148(n).

Example

a(4) = (3*5*7*11) - (3+5+7+11) = 1129.

Maple

a:= n-> (l-> mul(i, i=l)-add(i, i=l))([ithprime(i)$i=2..n+1]):
seq(a(n), n=0..20);  # Alois P. Heinz, Jul 12 2022

Mathematica

FoldList[Times, 1, p = Prime[Range[2, 20]]] - Prepend[Accumulate[p], 0] (* Amiram Eldar, Jul 14 2022 *)

Prog

(Python)
from itertools import count, islice
from sympy import nextprime
def agen():
    p, s, primen = 1, 0, 2
    while True:
        yield p - s; primen = nextprime(primen); p *= primen; s += primen
print(list(islice(agen(), 19))) # Michael S. Branicky, Jul 12 2022
(PARI) a(n) = my(vp=primes(n+1)); vecprod(vp)/2 - vecsum(vp) + 2; \\ Michel Marcus, Jul 12 2022

Crossrefs

Cf. A000040, A059841, A070826, A071148, A355590.

Sequence in context: A200832 A103064 A244849 * A360914 A321164 A243699

Adjacent sequences: A355588 A355589 A355590 * A355592 A355593 A355594

Keyword

nonn

Author

Des MacHale and Bernard Schott, Jul 12 2022

Extensions

More terms from Michael S. Branicky, Jul 12 2022

Status

approved