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A130912
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Fermat quotients, mod p: ((2^(p-1) - 1)/p) mod p = A007663(n) mod p.
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2
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1, 3, 2, 5, 3, 13, 3, 17, 1, 6, 1, 23, 25, 44, 36, 8, 36, 10, 2, 56, 19, 48, 6, 57, 92, 59, 13, 67, 83, 18, 17, 53, 30, 96, 56, 82, 67, 47, 3, 50, 148, 50, 104, 175, 135, 109, 189, 201, 68, 7, 26, 142, 247, 225, 128, 260, 109, 70, 74, 58, 78, 294, 175, 120, 175, 139, 153
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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REFERENCES
| Paulo Ribenboim, "The Little Book of Begger Primes", Springer-Verlag, 2004, p. 232.
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FORMULA
| Fermat quotients mod p = A007663: (1, 3, 9, 93, 315,...) mod p; where the Fermat quotients for base 2 = (2^(p-1) - 1). Applies to the odd primes.
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EXAMPLE
| a(4) = 2 = 9 mod 7 where A007663(4) = 9.
The Fermat prime(base 2) for 7 = 9 = (2^6 - 1)/7. Then 9 mod 7 = 2.
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MAPLE
| a := 2 : for n from 2 to 120 do p := ithprime(n) ; fq := (a^(p-1)-1)/p ; printf("%d, ", fq mod p) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2008]
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CROSSREFS
| Cf. A007663.
Sequence in context: A131025 A070151 * A178844 A143956 A110661 A143124
Adjacent sequences: A130909 A130910 A130911 * A130913 A130914 A130915
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 08 2007
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2008
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