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Search: id:A111055
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| A111055 |
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Minimal set of prime-strings in base 10 for primes of the form 4n+1 in the sense of A071062. |
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+0
2
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| 5, 13, 17, 29, 37, 41, 61, 73, 89, 97, 101, 109, 149, 181, 233, 277, 281, 349, 409, 433, 449, 677, 701, 709, 769, 821, 877, 881, 1669, 2221, 3001, 3121, 3169, 3221, 3301, 3833, 4969, 4993, 6469, 6833, 6949, 7121, 7477, 7949, 9001, 9049, 9221, 9649, 9833
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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Walter A. Kehowski, Full list of terms
J. Shallit, Minimal primes, J. Recreational Mathematics, vol. 30.2, pp. 113-117, 1999-2000.
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EXAMPLE
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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.
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MAPLE
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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
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CROSSREFS
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Cf. A071062, A071070, A110600, A110615.
Sequence in context: A113482 A077426 A002144 this_sequence A145016 A123079 A038938
Adjacent sequences: A111052 A111053 A111054 this_sequence A111056 A111057 A111058
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KEYWORD
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base,fini,nonn,uned
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AUTHOR
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Walter A. Kehowski (wkehowski(AT)cox.net), Oct 06 2005
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