## Prime Like Sequences

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• The sequence of primes have certain characteristic properties. Other sequences of integers have properties in common with the sequence of primes. One family of
Message 1 of 1 , Jun 8, 2008
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The sequence of primes have certain characteristic properties.

Other sequences of integers have properties in common with the sequence
of primes.

One family of such integer sequences is defined as follows:

Define the sequence

q_p(i) = {(p_i - p)/2 : p_i > p }

where p is an odd prime, p_i is the ith odd prime.

q_3(i) = {1, 2,4,5,7,8,10,13,14,17,19,20 . . . }

q_5{i} = {1,3,4,6,7,9,12,13,16,18,19. . .}

q_7{i} = {2,3,5,6,8,11,12,15,17,18. . .}

q_11{i} = {1,3,4,6,9,10,13,15,16. . .}

etc

What makes these sequences prime like?

They will have distribution properties describable in terms of the
natural logarithm,
and also each successor term will be apparently unpredictable from any
trending of the previous terms.

Kermit Rose

< kermit@... >
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