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A362882 Number of even numbers generated by adding two distinct odd primes <= prime(n+1).

%I A362882 #28 May 15 2023 21:50:10
%S A362882 0,1,3,6,8,11,14,17,20,25,28,33,37,40,44,47,53,57,62,66,70,75,79,85,
%T A362882 89,93,98,102,106,113,117,122,129,134,140,145,150,157,161,166,172,176,
%U A362882 181,186,191,196,202,210,214,221,225,230,236,241,245,248,256,264
%N A362882 Number of even numbers generated by adding two distinct odd primes <= prime(n+1).
%e A362882 For n = 3, the primes are 3, 5 and 7. 3 + 5 = 8, 3 + 7 = 10 and 5 + 7 = 12 are all distinct even numbers, so a(3) = 3.
%o A362882 (Python)
%o A362882 from sympy import nextprime
%o A362882 from itertools import islice
%o A362882 def agen(): # generator of terms
%o A362882     plst, s, p = [3], set(), 3
%o A362882     while True:
%o A362882         yield len(s)
%o A362882         p = nextprime(p)
%o A362882         s.update(p+pi for pi in plst)
%o A362882         plst.append(p)
%o A362882 print(list(islice(agen(), 60))) # _Michael S. Branicky_, May 07 2023
%Y A362882 First differences give A083060.
%K A362882 nonn
%O A362882 1,3
%A A362882 _Kshitij Thakkar_ and _Gargee Girdhari_, May 07 2023