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A242992 Least k>n/2, k<n, such that 2^(n-k)-1 divides 2^k-2, or 0 if no such k exists. 0
0, 0, 0, 2, 3, 3, 5, 4, 7, 5, 7, 6, 11, 7, 13, 8, 11, 9, 17, 10, 19, 11, 15, 12, 23, 13, 21, 14, 19, 15, 29, 16, 31, 17, 23, 18, 29, 19, 37, 20, 27, 21, 41, 22, 43, 23, 31, 24, 47, 25, 43, 26, 35, 27, 53, 28, 45, 29, 39, 30, 59, 31, 61, 32, 43, 33, 53, 34, 67, 35, 47, 36, 71, 37, 73, 38, 51, 39, 67, 40, 79, 41, 55, 42, 83, 43, 69, 44, 59, 45, 89, 46, 79 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Related to the search of primitive weird numbers A006037 of the form 2^(k-1)*Q*R with Q=2^n-1 and R=(2^k*Q-Q-1)/(Q+1-2^k). (Of course only primes n can lead to a (Mersenne) prime Q (cf. A000043), and R must also be prime to get a weird number.)

For n>2, there always exists auch a k=a(n)>0, since k=n-1 trivially satisfies the condition (2^(n-k)-1 = 1).

For odd indices n>2, k=a(n)=(n+1)/2 since this is the least k>n/2 and 2^(k-1)-1 divides 2^k-2.

LINKS

Table of n, a(n) for n=0..92.

FORMULA

For n = 2m-1 > 2, a(n) = m.

For all n, a(n) <= n-1, and equality holds when n-1 is a prime.

CROSSREFS

Sequence in context: A064916 A062854 A057859 * A029579 A106647 A130157

Adjacent sequences:  A242989 A242990 A242991 * A242993 A242994 A242995

KEYWORD

nonn

AUTHOR

M. F. Hasler, Aug 17 2014

STATUS

approved

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)