[seqfan] Re: A Composition

Jack Brennen jfb at brennen.net
Wed Apr 10 21:16:21 CEST 2013


Base 10 looks good to me.  I get the continuation:

2, 5, 11, 13, 29, 31, 17, 19, 43, 7, 37, 41, 71, 47, 67, 89, 3, 101, 23, 
109, 59, 83, 103, 73, 107, 157, 53, 127, 149, 61, 131, 139, 79, 163, 
191, 193, 97, 113, 137, 167, 211, 181, 151, 197, 199, 173, 223, 239, 
227, 179, 241, 251, 229, 257, 313, 233, 263, 277, 271, 283, 307, 347, 
269, 293, 281, 349, 401, 397, 367, 383, 431, 337, 353, 379, 331, 419, 
359, 439, 487, 311, 373, 409, 457, 461, 421, 317, 463, 389, 467, 433, 
499, 443, 521, 541, 479, 547, 503, 557, 491, 569, 523

Of course, the assumption that it is a permutation may be a safe
conjecture, but probably beyond proof.


On 4/10/2013 11:28 AM, Hans Havermann wrote:
> I wonder if someone might confirm for me the lexicographically first permutation of the primes in which the concatenation of any number of consecutive terms is composite. I have:
>
> 2, 5, 11, 13, 29, 31, 17, 19, 43, 7, 37, 41, 71, 47, 67, 89, 3, 101, 23, 109, 59, 83, 103, 73, 107, 157, 53, 127, 149, 61, 131, 139, 79, 163, 191, 193, 97, 113, 137, 167, 211, 181, …
>
> In base-two:
>
> 2, 5, 17, 13, 11, 23, 3, 19, 7, 53, 37, 31, 47, 29, 43, 59, 41, 73, 67, 83, 89, 61, 79, 71, 107, 97, 127, 131, 101, 113, 151, 103, 137, 109, 167, 179, 139, 227, 149, 191, 157, 193, …
>
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