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A016048 Least k such that (2*p_n)*k + 1 | Mersenne(p_n), p_n = n-th prime, n >= 2. 0

%I

%S 1,3,9,1,315,3855,13797,1,4,34636833,3,163,5,25,60,1525,

%T 18900352534538475,1445580,1609,3,17,1,3477359660913989536233495,59,

%U 36793758459,12379533,758220919762679268184943973309,3421967,15

%N Least k such that (2*p_n)*k + 1 | Mersenne(p_n), p_n = n-th prime, n >= 2.

%C M(p_n) = 2^p_n - 1 = (2*p_n)*j + 1 = [(2*p_n)*k_1 + 1] ... [(2*p_n)*k_i + 1], n >= 2 (i.e. odd prime p_n), i >= 1. Then k = Min(k_1, ..., k_i).

%H Chris K. Caldwell, <a href="http://primes.utm.edu/notes/proofs/MerDiv.html">Modular restrictions on Mersenne divisors</a>

%F a(n) = (A016047(n) - 1) / (2*A000040(n)). - _Jeppe Stig Nielsen_, Jul 18 2014

%K nonn

%O 2,2

%A _Robert G. Wilson v_

%E Definition edited, comment added by _Daniel Forgues_, Oct 06 2009

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Last modified April 9 10:32 EDT 2020. Contains 333348 sequences. (Running on oeis4.)