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%I #21 Nov 02 2023 16:01:53
%S 0,3,2,1,3,1,2,1,2,2,2,1,2,1,2,4,3,7,1,4,3,1,2,1,1,2,1,3,1,4,1,2,2,5,
%T 2,2,6,1,2,5,3,2,7,1,2,1,1,1,3,1,3,5,2,2,3,2,2,2,1,2,6,3,1,4,1,3,2,2,
%U 3,1,3,1,2,4,1,2,1,1,1,2,3,2,5,3,1,2,1,1,2,1,1,1,1,1,1,2,1,2,3,6,4,5,2,2,2,2,2,3,4,3,2,1,2,1,3,2,1,2,5,3,1,1,4
%N a(n) = 2-adic valuation of prime(n)+prime(n+1).
%H Charles R Greathouse IV, <a href="/A237881/b237881.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A007814(A001043(n)).
%F a(n) << log n; in particular, a(n) <= log_2 n + log_2 log n + O(1). - _Charles R Greathouse IV_, Feb 14 2014
%e a(5)=3 because prime(5)=11, prime(6)=13, 11+13=24=2^3*3, 2-adic valuation(24)=3.
%t IntegerExponent[ListConvolve[{1,1},Prime[Range[200]]],2] (* _Paolo Xausa_, Nov 02 2023 *)
%o (PARI) {for(i=1,200,k=valuation(prime(i)+prime(i+1),2);print1(k,", "))}
%o (Python)
%o from sympy import prime
%o def A237881(n): return (~(m:=prime(n)+prime(n+1))&m-1).bit_length() # _Chai Wah Wu_, Jul 08 2022
%Y Cf. A071087, A098048.
%K nonn,easy
%O 1,2
%A _Antonio Roldán_, Feb 14 2014
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