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A268353 a(n) is the exponent of 2 corresponding to the n-th Proth prime.

%I A268353 #6 Feb 03 2016 02:47:59
%S A268353 1,2,2,4,3,5,4,6,4,8,5,6,6,7,5,8,5,7,6,7,6,6,7,6,6,8,7,7,7,7,7,9,8,8,
%T A268353 7,7,7,9,7,9,7,12,10,7,7,8,8,7,10,7,9,11,10,8,9,8,10,9,8,8,8,9,8,9,8,
%U A268353 10,10,8,13,8,8,9,8,8,8,10,9,8,8,10,11
%N A268353 a(n) is the exponent of 2 corresponding to the n-th Proth prime.
%C A268353 a(n) = m where A080076(n) = k*2^m + 1, k odd.
%H A268353 Robert Israel, <a href="/A268353/b268353.txt">Table of n, a(n) for n = 1..10000</a>
%F A268353 a(n) = A007814(A080076(n)-1).
%e A268353 The first Proth prime A080076(1) = 3 = 1*2^1 + 1, so a(1) = 1.
%e A268353 The second Proth prime A080076(2) = 5 = 1*2^2 + 1, so a(2) = 2.
%p A268353 N:= 10^6: # for all Proth primes <= N
%p A268353 Proth:= sort(convert(select(isprime, {seq(seq(k*2^m+1, k = 1 .. min(2^m, (N-1)/2^m), 2), m=1..ilog2(N-1))}),list)):
%p A268353 map(t -> padic:-ordp(t-1,2), Proth);
%Y A268353 Cf. A007814, A080076.
%K A268353 nonn
%O A268353 1,2
%A A268353 _Robert Israel_, Feb 02 2016