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

Author

Simon Strandgaard, Jan 14 2021

Keywords

• nonn
• look

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.

Crossrefs

Cf. A000040, A117495, A340128.

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