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Search: id:A111056
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| A111056 |
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Minimal set of prime-strings in base 10 for primes of the form 4n+3 in the sense of A071062. |
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+0
1
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| 3, 7, 11, 19, 59, 251, 491, 499, 691, 991, 2099, 2699, 2999, 4051, 4451, 4651, 5051, 5651, 5851, 6299, 6451, 6551, 6899, 8291, 8699, 8951, 8999, 9551, 9851, 22091, 22291, 66851, 80051, 80651, 84551, 85451, 86851, 88651, 92899, 98299, 98899
(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)=2099 since the pattern "*2*0*9*9*" does not occur in any previously found prime of the form 4n+3. Assuming all previous members of the list have been similarly recursively constructed, then 2099 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; M3:=[]: wcM3:=[]: 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 = 3 then sp:=convert(p, string); if andmap(proc(w) not(WildcardMatch(w, sp)) end, wcM3) then M3:=[op(M3), p]; wcM3:=[op(wcM3), 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: A132449 A132453 A060288 this_sequence A083908 A050577 A095352
Adjacent sequences: A111053 A111054 A111055 this_sequence A111057 A111058 A111059
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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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