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Search: id:A086000
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| A086000 |
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For p = prime(n), a(n) is the smallest N such that pN is a base-2 pseudoprime (that is, 2^(pN-1) = 1 mod pN). |
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3
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| 187, 129, 247, 31, 85, 33, 73, 89, 85, 11, 73, 161, 15, 93, 157, 233, 481, 133, 281, 19, 391, 1067, 23, 193, 601, 307, 6361, 37, 29, 15, 2731, 545, 10213, 593, 31, 53, 2593, 499, 1205, 141155, 1261, 2281, 97, 3333, 1387, 1891, 1777, 3391, 381, 59, 20231, 97
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Tables compiled by Pinch were used. Sequence A085999 lists a(n)*prime(n). It can be shown that a(n) has the form 1 + 2 ord(4, prime(n)) k for some k > 0, where the ord(x,y) function is the smallest positive integer r such that x^r = 1 mod y. The value of k for a(n) is given in sequence A086001. Note that prime(n) divides 2^a(n) - 2. Compare A085012, which gives the smallest prime q such that pq is a 2-pseudoprime.
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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(2) = 187 because prime(2) = 3 and N=187 is the smallest number such that 3N is a 2-pseudoprime.
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MATHEMATICA
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Table[p=Prime[n]; m=MultiplicativeOrder[4, p]; k=1; While[psp=p(1+2*m*k); PowerMod[2, psp-1, psp]!=1, k++ ]; 1+2*m*k, {n, 2, 100}]
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CROSSREFS
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Cf. A001567 (base-2 pseudoprimes), A082654 (ord(4, p)), A085012, A085999, A086001.
Adjacent sequences: A085997 A085998 A085999 this_sequence A086001 A086002 A086003
Sequence in context: A015273 A124207 A068257 this_sequence A081703 A029556 A045224
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KEYWORD
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easy,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jul 08 2003
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