Sequence A080611: Lowest Base with Primality test for first N primes

This sequence, Sloane's A080611, gives the lowest base of a number system in which it is easy to test for the first N prime divisors.

For example, in base 10 it is easy to test for divisibility by 2 and 5 (by checking te last digit), by 3 (by casting out 9's), and by 11 (by alternately adding and subtracting the digits and noting if the answer is a multiple of 11, for example, to test 132: 1-3+2=0, therefore 132 is a multiple of 11.

So base 10 has tests for 2, 3, 5 and 11: the first three primes and one other. But in base 6, the same tests tell if a number is divisible by 2, 3, 5, and 7: the first 4 primes. Base 6 is the first base with tests for the first 4 primes, and thus 6 is the 4th term in the sequence.

The sequence runs: 2, 2, 4, 6, 21, 155, 441, 2925, 10165, 342056, 2781505, 10631544, 163886800, 498936010, 5163068911, 794010643700, 17635639237580, 353823355745574, 16828233620277430, 224220167903546529, 11990471619719586785, 113367767003198032480, 4446177962278202834685, 118332081735203144063619, 1103720538399012083835935, 78239926422758111576984420, ...

Another similar sequence is discussed here.

Some other sequences are discussed here.

This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2014 Dec 07.

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