A340649 a(n) = (n*prime(n+1)) mod prime(n).
1, 1, 1, 2, 10, 11, 14, 13, 8, 20, 4, 11, 26, 13, 43, 43, 34, 47, 9, 40, 53, 9, 55, 14, 3, 52, 5, 56, 7, 81, 124, 61, 66, 62, 70, 65, 65, 152, 67, 67, 82, 58, 86, 176, 90, 154, 142, 192, 98, 200, 73, 104, 48, 73, 73, 73, 114, 77, 236, 120, 44, 282, 252, 128
Offset: 1
Examples
a(1) = (prime(1+1) * 1) mod prime(1) = 3 * 1 mod 2 = 1, a(2) = (prime(2+1) * 2) mod prime(2) = 5 * 2 mod 3 = 1, a(3) = (prime(3+1) * 3) mod prime(3) = 7 * 3 mod 5 = 1, a(4) = (prime(4+1) * 4) mod prime(4) = 11 * 4 mod 7 = 2, a(5) = (prime(5+1) * 5) mod prime(5) = 13 * 5 mod 11 = 10.
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
- Simon Strandgaard, Animations of ((n+k)*prime(n+1)) mod prime(n) when k varies, YouTube video, 2021.
Programs
-
Magma
[ (n*NthPrime(n+1)) mod NthPrime(n) : n in [1..60]]; // Wesley Ivan Hurt, Apr 23 2021
-
Mathematica
Table[Mod[Prime[n + 1]*n, Prime[n]],{n, 1, 64}] (* Robert P. P. McKone, Jan 15 2021 *) -
PARI
a(n) = prime(n+1)*n % prime(n); \\ Michel Marcus, Jan 15 2021
-
Ruby
require 'prime' values = [] primes = Prime.first(20) primes.each_index do |n| next if n < 1 values << (primes[n] * n) % primes[n-1] end p values
Formula
a(n) = A117495(n+1) mod prime(n). - Michel Marcus, Jan 15 2021