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A069830
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Multiplicative inverse of prime(n) modulo prime(n+1).
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7
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2, 2, 3, 8, 6, 4, 9, 17, 24, 15, 6, 10, 21, 35, 44, 49, 30, 11, 53, 36, 13, 62, 74, 12, 25, 51, 80, 54, 28, 9, 98, 114, 69, 134, 75, 26, 27, 125, 144, 149, 90, 19, 96, 49, 99, 123, 130, 170, 114, 58, 199, 120, 25, 214, 219, 224, 135, 46, 70, 141, 205, 285, 233, 156, 79
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OFFSET
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1,1
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COMMENTS
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Smallest k such that prime(n+1) divides k*prime(n) - 1, n>1.
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LINKS
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FORMULA
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EXAMPLE
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a(4) = 8 as prime(5) = 11 divides 8*7 -1, where 7 = prime(4).
a(9) = 24, for a(9)*prime(9) = 24*23 = (-5)*(-6) [mod 29] = 1 [mod prime(10)].
a(14) = 35, for a(14)*prime(14) = 35*43 = (-12)*(-4) [mod 47] = 1 [mod prime(15)].
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MAPLE
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seq( (1/ithprime(n) mod ithprime(n+1)), n = 1..65); # G. C. Greubel, Aug 09 2019
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MATHEMATICA
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Table[PowerMod[Prime[n], -1, Prime[n+1]], {n, 65}] (* G. C. Greubel, Aug 09 2019 *)
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PROG
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(PARI) vector(65, n, lift(Mod(prime(n), prime(n+1))^-1)) \\ Joerg Arndt, Aug 09 2019
(Magma) [InverseMod(NthPrime(n), NthPrime(n+1)): n in [1..65]]; // G. C. Greubel, Aug 09 2019
(Sage) [nth_prime(n).inverse_mod(nth_prime(n+1)) for n in (1..65)] # G. C. Greubel, Aug 09 2019
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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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STATUS
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approved
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