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A001134
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Primes p such that the multiplicative order of 2 modulo p is (p-1)/4.
(Formerly M5371 N2332)
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12
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113, 281, 353, 577, 593, 617, 1033, 1049, 1097, 1153, 1193, 1201, 1481, 1601, 1889, 2129, 2273, 2393, 2473, 3049, 3089, 3137, 3217, 3313, 3529, 3673, 3833, 4001, 4217, 4289, 4457, 4801, 4817, 4937, 5233, 5393, 5881, 6121, 6521, 6569, 6761, 6793, 6841, 7129, 7481, 7577, 7793, 7817, 7841, 8209
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OFFSET
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1,1
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COMMENTS
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The multiplicative order of x modulo y is the smallest positive number m such that x^m is congruent to 1 mod y.
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REFERENCES
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M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 59.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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Reap[For[p = 2, p <= 6761, p = NextPrime[p], If[ MultiplicativeOrder[2, p] == (p-1)/4, Sow[p]]]][[2, 1]] (* Jean-François Alcover, May 17 2013 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(6761) | r eq 1 and Order(R!2) eq q where q, r is Quotrem(p, 4) where R is ResidueClassRing(p) ]; // Klaus Brockhaus, Dec 02 2008
(PARI) forprime(p=3, 10^4, if(znorder(Mod(2, p))==(p-1)/4, print1(p, ", "))); \\ Joerg Arndt, May 17 2013
(PARI) oddres(n)=n>>valuation(n, 2)
cyc(d)=my(k=1, t=1, y=(d-5)/(2*3)+1); while((t=oddres(t+d))>1 && k<=y, k++); k
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms and better definition from Don Reble, Mar 11 2006
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STATUS
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approved
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