%I A111055
%S A111055 5,13,17,29,37,41,61,73,89,97,101,109,149,181,233,277,281,349,409,433,
%T A111055 449,677,701,709,769,821,877,881,1669,2221,3001,3121,3169,3221,3301,
%U A111055 3833,4969,4993,6469,6833,6949,7121,7477,7949,9001,9049,9221,9649,9833
%N A111055 Minimal set of prime-strings in base 10 for primes of the form 4n+1 in 
               the sense of A071062.
%C A111055 I think the list is complete since I have flow-charted many of the possibilites 
               and I am in the process of checking in the range 10^11 < p < 10^12 
               but it will take a while.
%H A111055 Walter A. Kehowski, <a href="a111055.txt">Full list of terms</a>
%H A111055 J. Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/Papers/minimal5.ps">
               Minimal primes</a>, J. Recreational Mathematics, vol. 30.2, pp. 113-117, 
               1999-2000.
%e A111055 a(11)=101 since the pattern "*1*0*1*" does not occur in any previously 
               found prime of the form 4n+1. Assuming all previous members of the 
               list have been similarly recursively constructed, then 109 is the 
               next prime in the list. The basic rule is: if no substring of p matches 
               any previously found prime, add p to the list. The basic theorem 
               of minimal sets says that this process will terminate, that is, the 
               minimal set is always finite.
%p A111055 with(StringTools); wc := proc(s) cat("*",Join(convert(s,list),"*"),"*") 
               end; M1:=[]: wcM1:=[]: p:=1: for z from 1 to 1 do for k while p<10^11 
               do p:=nextprime(p); if k mod 100000 = 0 then print(k,p,evalf((time()-st)/
               60,4)) fi; if p mod 4 = 1 then sp:=convert(p,string); if andmap(proc(w) 
               not(WildcardMatch(w,sp)) end, wcM1) then M1:=[op(M1),p]; wcM1:=[op(wcM1),
               wc(sp)]; print(p) fi fi od od; # let it run for a couple of days
%Y A111055 Cf. A071062, A071070, A110600, A110615.
%Y A111055 Sequence in context: A113482 A077426 A002144 this_sequence A145016 A123079 
               A038938
%Y A111055 Adjacent sequences: A111052 A111053 A111054 this_sequence A111056 A111057 
               A111058
%K A111055 base,fini,nonn,uned
%O A111055 1,1
%A A111055 Walter A. Kehowski (wkehowski(AT)cox.net), Oct 06 2005