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A332657 Alternate adding and multiplying prime numbers: a(2n) = a(2n-1) * prime(2n+1) and a(2n-1) = a(2n) + prime(2n-2) for n >= 1.

%I A332657 #24 Mar 21 2023 12:13:08
%S A332657 5,25,32,352,365,6205,6224,143152,143181,4438611,4438648,181984568,
%T A332657 181984611,8553276717,8553276770,504643329430,504643329491,
%U A332657 33811103075897,33811103075968,2468210524545664,2468210524545743,204861473537296669,204861473537296758
%N A332657 Alternate adding and multiplying prime numbers: a(2n) = a(2n-1) * prime(2n+1) and a(2n-1) = a(2n) + prime(2n-2) for n >= 1.
%e A332657 a(1) = 2 + 3 = 5;
%e A332657 a(2) = 5 * 5 = 25;
%e A332657 a(3) = 25 + 7 = 32;
%e A332657 ...
%e A332657 a(40) = 2714410084880275101596278688487175846.
%o A332657 (Python)
%o A332657 from sympy import primerange
%o A332657 p = list(primerange(1, 200))
%o A332657 def a(n):
%o A332657     out = p[0] + p[1]
%o A332657     for i in range(1, n):
%o A332657         if i % 2:
%o A332657             out *= p[i + 1]
%o A332657         else:
%o A332657             out += p[i + 1]
%o A332657     return out
%o A332657 for n in range(1, 25):
%o A332657     print(a(n), end=", ")
%Y A332657 Cf. A047905, A047904, A077138, A222559, A332659, A332660.
%K A332657 nonn,easy
%O A332657 1,1
%A A332657 _Adnan Baysal_, Feb 18 2020