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A317029
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Invertible primes p such that k*p - 1 and k*p + 1 is a twin prime pair; for k = 12.
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0
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19, 601, 1601, 16661, 16981, 19609, 60689, 66809, 69001, 69011, 100169, 119191, 189901, 196919, 616961, 1061689, 1088089, 1091119, 1106069, 1196089, 1198069, 1611601, 1666019, 1688969, 1800119, 1861889, 1891619, 1891661, 1910669, 1996681, 6060091, 6160601, 6196909
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OFFSET
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1,1
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COMMENTS
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k = 12 is the smallest integer to produce such sequence.
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LINKS
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EXAMPLE
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a(2) = 601 is an invertible prime; 12*601 - 1 = 7211; 12*601 + 1 = 7213; 7211 and 7213 form a twin prime pair.
a(4) = 16661 is an invertible prime; 12*16661 - 1 = 199931; 12*16661 + 1 = 199933; 199931 and 199933 form a twin prime pair.
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MATHEMATICA
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k = 12; Select[lst = {};
fQ[n_] := Block[{allset = {0, 1, 6, 8, 9}, id = IntegerDigits@n}, rid = Reverse[id /. {6 -> 9, 9 -> 6}]; Union@Join[id, allset] == allset && PrimeQ@FromDigits@rid && rid != id]; Do[If[PrimeQ@n && fQ@n, AppendTo[lst, n]], {n, 12000000}]; lst,
PrimeQ[k# + 1] && PrimeQ[k# - 1] &]
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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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