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A268353 a(n) is the exponent of 2 corresponding to the n-th Proth prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A145393 A215675 A132802 * A204900 A070803 A071693

Adjacent sequences:  A268350 A268351 A268352 * A268354 A268355 A268356

KEYWORD

nonn

AUTHOR

Robert Israel, Feb 02 2016

STATUS

approved

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Last modified October 23 06:29 EDT 2018. Contains 316520 sequences. (Running on oeis4.)