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A077005 Smallest k such that prime(n) divides k*prime(n-1) + 1, n > 1. 3

%I

%S 1,3,4,3,7,13,10,6,5,16,31,31,22,12,9,10,31,56,18,37,66,21,15,85,76,

%T 52,27,55,85,118,33,23,70,15,76,131,136,42,29,30,91,172,97,148,100,88,

%U 93,57,115,175,40,121,226,43,44,45,136,231,211,142,88,22,78,157,238,71,281

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

%C a(n) = inverse of (prime(n)-prime(n-1)) mod prime(n). This is the least k such that prime(n)|k*((prime(n)-prime(n-1))-1). Since prime(n)|k*prime(n), it must divide (k*prime(n-1)+1), so k = a(n). Also, a(n) = prime(n) - (x*prime(n)+1)/prime(n-1) for the least such x. - _David James Sycamore_, Oct 05 2018

%F a(n) = prime(n+1) - A069830(n). - _Emmanuel Vantieghem_, Aug 12 2018

%e a(4) = 3 as prime(5) = 11 divides 3*7 + 1, where 7 = prime(4).

%t sk[a_,b_]:=Module[{k=1},While[!Divisible[k*a+1,b],k++];k]; sk@@@ Partition[ Prime[Range[70]],2,1] (* _Harvey P. Dale_, Jun 23 2013 *)

%o (PARI) a(n) = {my(k = 1, p = prime(n-1), q = prime(n)); while ((k*p+1) % q, k++); k;} \\ _Michel Marcus_, Aug 14 2018

%Y Cf. A069830.

%K nonn,easy

%O 2,2

%A _Amarnath Murthy_, Oct 26 2002

%E More terms from _Ralf Stephan_, Oct 31 2002

%E More terms from _Ray Chandler_, Oct 24 2003

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Last modified November 13 10:29 EST 2019. Contains 329093 sequences. (Running on oeis4.)