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

1,2

Comments

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

Links

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

Formula

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

Example

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.

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);

Crossrefs

Cf. A007814, A080076.

Sequence in context: A329439 A132802 A341947 * A204900 A070803 A071693

Adjacent sequences: A268350 A268351 A268352 * A268354 A268355 A268356

Keyword

nonn

Author

Robert Israel, Feb 02 2016

Status

approved