A194367 Smallest k such that prime(n) divides k*prime(n+1)+1.

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, 77, 53, 27, 8, 95, 109, 68, 125, 74, 25, 26, 122, 139, 144, 89, 18, 95, 48, 98, 116, 123, 167, 113, 57

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 23 2011

Keywords

• nonn
• easy

Examples

			a(4) = 5 as prime(4)=7 divides 5*11+1, where 11=prime(5).
a(7) = 8 = (17*9-1)/19. - _Bob Selcoe_, Aug 21 2016
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A077005.

Cf. A000040 (prime numbers), A069830.

Programs

Maple

seq(-ithprime(i+1)^(-1) mod ithprime(i),i=1..100); # Robert Israel, Aug 25 2016

Mathematica

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

PARI

a(n)=my(p=prime(n),q=nextprime(p+1));lift(Mod(-1,p)/q) \\ Charles R Greathouse IV, Sep 03 2011

Formula

a(n) = (prime(n)*A069830(n) - 1)/prime(n+1). - Bob Selcoe, Aug 21 2016