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A224929
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Primes such that concatenation of two adjacent terms and two adjacent digits is also prime.
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2
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2, 3, 7, 19, 73, 1117, 31, 37, 97, 373, 13, 1171, 11131, 11113, 79, 71713, 17137, 11173, 11719, 717979, 71719, 731173, 111373, 11197, 313, 71971, 11731, 13171, 11119, 731737, 113719, 719731, 379, 737119, 797119, 7171111, 37117, 19717, 11311, 97117, 17971
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OFFSET
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1,1
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COMMENTS
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Conjecture: all prime congruent to 1 (mod 3) which only have the odd digits {1, 3, 7, 9} but not 5 eventually appear. So far 139, 193, 199, 331, 337, 397, 733, 739, 919, 937, 991, 997, etc. have not appeared. - Robert G. Wilson v, May 06 2014
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LINKS
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FORMULA
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a(n) is the smallest prime not yet used which fits the conditions.
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EXAMPLE
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a(6)=1117 because it is a prime, 731117 is a prime, 31, 11, 11 and 17 are prime and no smaller and as-yet-unused prime satisfies the conditions.
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MATHEMATICA
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f[s_List] := Block[{id, p = s[[-1]], q = 3}, While[ pq = p*10^Floor[1 + Log10@ q] + q; id = IntegerDigits@ pq; Union@ Join[{1, 3, 7, 9}, id] != {1, 3, 7, 9} || MemberQ[s, q] || Union@ PrimeQ[ Join[ {pq}, FromDigits@# & /@ Partition[id, 2, 1]]] != {True}, q = NextPrime@ q]; Append[s, q]]; Nest[f, {2, 3}, 39] (* Robert G. Wilson v, May 06 2014 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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