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 November 4th, 2018, 04:28 AM #41 Senior Member   Joined: Aug 2008 From: Blacksburg VA USA Posts: 352 Thanks: 7 Math Focus: primes of course mild guesstimate I wonder if the values spoken of (11,23,47,2351,4703,??) will appear in the order seen in the Rowland sequence (A221869) ? Very limited dataset to make this guess, but ...
November 6th, 2018, 05:39 AM   #42
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 Originally Posted by billymac00 I wonder if the values spoken of (11,23,47,2351,4703,??) will appear in the order seen in the Rowland sequence (A221869) ? Very limited dataset to make this guess, but ...
Sounds probable to me too.

Speaking of which, we also might add that a necessary (but not sufficient) condition for odd n to be a prime is that $2^{(n-1)/2}$ mod $n = n-1$ $or$ $1$.

In addition, in the sequence you quoted above, call it {$a_i$}, $a_{i+1}$ = $2a_ik + 1$.

November 7th, 2018, 05:23 AM   #43
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 Originally Posted by penrose In addition, in the sequence you quoted above, call it {$a_i$}, $a_{i+1}$ = $2a_ik + 1$.
Edit: I should put an index on k as well: $a_{i+1}$ = $2a_ik_i + 1$

December 23rd, 2018, 05:52 AM   #44
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Quote:
 Originally Posted by billymac00 I wonder if the values spoken of (11,23,47,2351,4703,??) will appear in the order seen in the Rowland sequence (A221869) ? Very limited dataset to make this guess, but ...
Quote:
 Originally Posted by penrose In addition, in the sequence you quoted above, call it {$a_i$}, $a_{i+1}$ = $2a_ik + 1$. More about that later.
The sequence noted above (11,23,47,2351,4703,??) has been seeded with the prime 11. Suppose we seed with 3 instead. Then this sequence starts out as (3,7,127, etc.)

The first three are Mersenne primes. In fact, the sequence is an infinite sequence of Mersenne primes, defined by $m_1 = 3$, $m_{i+1} = 2^{m_i}-1$.

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