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Search: id:A086250
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| A086250 |
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Smallest base-2 Fermat pseudoprime x that has ord(2,x) = n, or 0 if one does not exist. |
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2
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| 0, 0, 0, 0, 0, 0, 0, 0, 0, 341, 2047, 0, 0, 5461, 4681, 4369, 0, 1387, 0, 13981, 42799, 15709, 8388607, 1105, 1082401, 22369621, 0, 645, 256999, 10261, 0, 16843009, 1227133513, 5726623061, 8727391, 1729, 137438953471, 91625968981, 647089, 561
(list; graph; listen)
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OFFSET
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1,10
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COMMENT
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A base-2 Fermat pseudoprime is a composite number x such that 2^x = 2 mod x. For such an x, ord(2,x) is the smallest positive integer m such that 2^m = 1 mod x. For a number x to have order n, it must be a factor of 2^n-1 and not be a factor of 2^r-1 for r<n. Sequence A086249 lists the number of pseudoprimes of order n.
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LINKS
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R. G. E. Pinch, Pseudoprimes and their factors (FTP)
Eric Weisstein's World of Mathematics, Pseudoprime
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EXAMPLE
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a(10) = 1 there is only 1 pseudoprime, 341 = 11*31, having order 10; that is, 2^10 = 1 mod 341.
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MATHEMATICA
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Table[d=Divisors[2^n-1]; num=0; i=1; done=False; While[m=d[[i]]; done=!PrimeQ[m]&&PowerMod[2, m, m]==2&&MultiplicativeOrder[2, m]==n; If[done, num=m]; !done&&i<Length[d], i++ ]; num, {n, 100}]
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CROSSREFS
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Cf. A001567 (base-2 pseudoprimes), A086249.
Adjacent sequences: A086247 A086248 A086249 this_sequence A086251 A086252 A086253
Sequence in context: A020230 A087716 A084653 this_sequence A069309 A086806 A006107
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KEYWORD
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hard,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jul 14 2003
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