A268353 - OEIS

%I #6 Feb 03 2016 02:47:59

%S 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 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 10,10,8,13,8,8,9,8,8,8,10,9,8,8,10,11

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

%C a(n) = m where A080076(n) = k*2^m + 1, k odd.

%H Robert Israel, <a href="/A268353/b268353.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A007814(A080076(n)-1).

%e The first Proth prime A080076(1) = 3 = 1*2^1 + 1, so a(1) = 1.

%e The second Proth prime A080076(2) = 5 = 1*2^2 + 1, so a(2) = 2.

%p N:= 10^6: # for all Proth primes <= N

%p 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 map(t -> padic:-ordp(t-1,2), Proth);

%Y Cf. A007814, A080076.

%K nonn

%O 1,2

%A _Robert Israel_, Feb 02 2016