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Smallest k such that prime(n) divides k*prime(n+1)+1.
1

%I #21 Aug 25 2016 20:45:24

%S 1,1,2,5,5,3,8,14,19,14,5,9,20,32,39,44,29,10,50,35,12,59,69,11,24,50,

%T 77,53,27,8,95,109,68,125,74,25,26,122,139,144,89,18,95,48,98,116,123,

%U 167,113,57

%N Smallest k such that prime(n) divides k*prime(n+1)+1.

%H Charles R Greathouse IV, <a href="/A194367/b194367.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (prime(n)*A069830(n) - 1)/prime(n+1). - _Bob Selcoe_, Aug 21 2016

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

%e a(7) = 8 = (17*9-1)/19. - _Bob Selcoe_, Aug 21 2016

%p seq(-ithprime(i+1)^(-1) mod ithprime(i),i=1..100); # _Robert Israel_, Aug 25 2016

%t Table[k = 1; While[! Divisible[k Prime[n + 1] + 1, Prime@ n], k++]; k, {n, 50}] (* _Michael De Vlieger_, Aug 22 2016 *)

%o (PARI) a(n)=my(p=prime(n),q=nextprime(p+1));lift(Mod(-1,p)/q) \\ _Charles R Greathouse IV_, Sep 03 2011

%Y Cf. A077005.

%Y Cf. A000040 (prime numbers), A069830.

%K nonn,easy

%O 1,3

%A _Juri-Stepan Gerasimov_, Aug 23 2011