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A122787
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a(n) is the smallest prime p such that the multiplicative order of 10 modulo p is 3^n.
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1
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3, 37, 333667, 757, 163, 411361786890737698932559, 313471, 2558791, 618846643, 2238862519, 396319276163359, 34720813
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| For n>0, a(n) is the smallest prime p>3 such that 3^n*p but not 3^(n-1)*p is a solution to 10^x==1 (mod x). A014950 gives solutions of this equation. It's obvious that if n is a term of A014950 then 3n is also a term of A014950. So according to the definition of a(n), for each m>n-1, 3^m*a(n) is in the sequence A014950.
a(12)>10^10, a(13)>10^10, a(14)=86093443.
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LINKS
| J. Brillhart et al., Factorizations of b^n +- 1), Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
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EXAMPLE
| p=333667 is the smallest prime such that multiplicative order of 10 modulo p is 3^2, so a(2)=333667.
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CROSSREFS
| Cf. A014950, A066364.
Sequence in context: A120480 A088098 A176245 * A093939 A129122 A002405
Adjacent sequences: A122784 A122785 A122786 * A122788 A122789 A122790
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KEYWORD
| hard,more,nonn
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AUTHOR
| Farideh Firoozbakht (mymontain(AT)yahoo.com), Oct 06 2006
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EXTENSIONS
| Revised and extended by Max Alekseyev (maxale(AT)gmail.com), Apr 25 2009
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