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A107126
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Numbers n such that (10^(2n+1)+45*10^n-1)/9 is prime.
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3
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OFFSET
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1,1
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COMMENTS
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n is in the sequence iff the palindromic number 1(n).6.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m + 1, 16m + 2, 16m + 5, 22m + 1, 22m + 9, etc. (the proof is easy).
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REFERENCES
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C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.
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LINKS
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FORMULA
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EXAMPLE
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14 is in the sequence because (10^(2*14+1)+45*10^14-1)/9=1(14).6.1(14) = 11111111111111611111111111111 is prime.
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MATHEMATICA
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Do[If[PrimeQ[(10^(2n + 1) + 45*10^n - 1)/9], Print[n]], {n, 2500}]
Position[Table[FromDigits[Join[PadRight[{}, n, 1], {6}, PadRight[{}, n, 1]]], {n, 1850}], _?PrimeQ]//Flatten (* Harvey P. Dale, Jun 22 2017 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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