%I #16 Jul 07 2022 16:18:37

%S 0,1,1,2,1,2,1,2,1,1,1,2,1,2,1,1,1,1,2,1,1,2,1,3,2,1,2,1,2,1,2,1,1,1,

%T 1,1,1,2,1,1,1,1,1,2,1,2,2,2,1,2,1,1,1,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,

%U 1,2,1,3,1,1,2,1,6,2,3

%N Exponent of 2 in prime factorization of prime(n)*prime(n-1) - 1.

%C a(n) = 1 if and only if A080378(n-1) = 2. - _Robert Israel_, Feb 07 2018

%H Robert Israel, <a href="/A023520/b023520.txt">Table of n, a(n) for n = 2..10000</a>

%F a(n) = A007814(A023515(n)). - _Michel Marcus_, Sep 30 2013

%p seq(padic:-ordp(ithprime(n)*ithprime(n-1)-1,2),n=2..200); # _Robert Israel_, Feb 07 2018

%o (PARI) a(n) = valuation(prime(n)*prime(n-1) - 1, 2); \\ _Michel Marcus_, Sep 30 2013

%o (Python)

%o from sympy import prime

%o def A023520(n): return (~(m:=prime(n)*prime(n-1)-1)& m-1).bit_length() # _Chai Wah Wu_, Jul 07 2022

%Y Cf. A007814, A023515, A080378.

%K nonn

%O 2,4

%A _Clark Kimberling_

%E Offset set to 2 and a(2) corrected by _Michel Marcus_, Sep 30 2013