A355591 - OEIS

%I #30 Jul 14 2023 15:20:40

%S 1,0,7,90,1129,14976,255199,4849770,111546337,3234846488,100280244907,

%T 3710369067210,152125131763369,6541380665834736,307444891294245379,

%U 16294579238595021986,961380175077106319097,58644190679703485491136,3929160775540133527938979

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

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

%H Robert Israel, <a href="/A355591/b355591.txt">Table of n, a(n) for n = 0..348</a>

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

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

%p a:= n-> (l-> mul(i,i=l)-add(i,i=l))([ithprime(i)$i=2..n+1]):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Jul 12 2022

%t FoldList[Times, 1, p = Prime[Range[2, 20]]] - Prepend[Accumulate[p], 0] (* _Amiram Eldar_, Jul 14 2022 *)

%o (Python)

%o from itertools import count, islice

%o from sympy import nextprime

%o def agen():

%o     p, s, primen = 1, 0, 2

%o     while True:

%o         yield p - s; primen = nextprime(primen); p *= primen; s += primen

%o print(list(islice(agen(), 19))) # _Michael S. Branicky_, Jul 12 2022

%o (PARI) a(n) = my(vp=primes(n+1)); vecprod(vp)/2 - vecsum(vp) + 2; \\ _Michel Marcus_, Jul 12 2022

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

%K nonn

%O 0,3

%A _Des MacHale_ and _Bernard Schott_, Jul 12 2022

%E More terms from _Michael S. Branicky_, Jul 12 2022