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A110600 Minimal set of prime-strings in base 12 in the sense of A071062. 4

%I

%S 2,3,5,7,11,13,73,97,109,577,1489,7537,17401,226201,1097113,32555521,

%T 388177921

%N Minimal set of prime-strings in base 12 in the sense of A071062.

%C Maple worksheet available upon request. Here is the minimal set in base 12 where X is 10 and E is 11. 2, 3, 5, 7, E, 11, 61, 81, 91, 401, X41, 4441, X0X1, XXXX1, 44XXX1, XXX0001, XX000001. This minimal set demonstrates the elegance of base 12 generally since you can mentally follow the process of elimination, all primes after E end in the neutral digit 1 and the last two entries only contain X, 0 and 1. There are no primes of the form X0...01 since the sum of its digits is E and hence it is divisible by E.

%C The smallest prime found to date that satisfies all patterns in the minimal set is 1234456789X04XXX00E0001 (656969693573113867991809 in base 10). [_Walter Kehowski_, May 18 2012]

%e a(10)=401 since no earlier prime in the list contained the pattern "*4*0*1*" where "*" stands for zero or more digits. The list can be manually constructed using a sieve-like process: eliminate all subsequent primes of the form "*4*0*1*" from the list of all primes. Assuming all previous elements have also been similarly determined, the next remaining prime should be X41.

%Y Cf. A071062, A071070.

%K nonn,base

%O 1,1

%A _Walter Kehowski_, Sep 14 2005

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Last modified June 15 13:47 EDT 2021. Contains 345048 sequences. (Running on oeis4.)