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

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, 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, 10, 10, 8, 13, 8, 8, 9, 8, 8, 8, 10, 9, 8, 8, 10, 11

Offset: 1

Author

Robert Israel, Feb 02 2016

Keywords

• nonn

Comments

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

Examples

			The first Proth prime A080076(1) = 3 = 1*2^1 + 1, so a(1) = 1.
The second Proth prime A080076(2) = 5 = 1*2^2 + 1, so a(2) = 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007814, A080076.

Programs

Maple

N:= 10^6: # for all Proth primes <= N
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)):
map(t -> padic:-ordp(t-1,2), Proth);

Formula

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