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A069830 Multiplicative inverse of prime(n) modulo prime(n+1). 6

%I

%S 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,

%T 51,80,54,28,9,98,114,69,134,75,26,27,125,144,149,90,19,96,49,99,123,

%U 130,170,114,58,199,120,25,214,219,224,135,46,70,141,205,285,233,156,79

%N Multiplicative inverse of prime(n) modulo prime(n+1).

%C Smallest k such that prime(n+1) divides k*prime(n) - 1, n>1.

%H G. C. Greubel, <a href="/A069830/b069830.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) + A077005(n) = prime(n+1). - _Emmanuel Vantieghem_, Aug 12 2018

%e a(4) = 8 as prime(5) = 11 divides 8*7 -1, where 7 = prime(4).

%e a(9) = 24, for a(9)*prime(9) = 24*23 = (-5)*(-6) [mod 29] = 1 [mod prime(10)].

%e a(14) = 35, for a(14)*prime(14) = 35*43 = (-12)*(-4) [mod 47] = 1 [mod prime(15)].

%p seq( (1/ithprime(n) mod ithprime(n+1)), n = 1..65); # _G. C. Greubel_, Aug 09 2019

%t Table[PowerMod[Prime[n], -1, Prime[n+1]], {n, 65}] (* _G. C. Greubel_, Aug 09 2019 *)

%o (PARI) vector(65,n,lift(Mod(prime(n),prime(n+1))^-1)) \\ _Joerg Arndt_, Aug 09 2019

%o (MAGMA) [InverseMod(NthPrime(n), NthPrime(n+1)): n in [1..65]]; // _G. C. Greubel_, Aug 09 2019

%o (Sage) [nth_prime(n).inverse_mod(nth_prime(n+1)) for n in (1..65)] # _G. C. Greubel_, Aug 09 2019

%Y Cf. A077005.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Apr 23 2002

%E More terms from _Rick L. Shepherd_, May 03 2002

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)