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

1,4

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.

Formula

a(n) = A117495(n+1) mod prime(n). - Michel Marcus, Jan 15 2021

Example

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.

Mathematica

Table[Mod[Prime[n + 1]*n, Prime[n]], {n, 1, 64}] (* Robert P. P. McKone, Jan 15 2021 *)

Prog

(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
(PARI) a(n) = prime(n+1)*n % prime(n); \\ Michel Marcus, Jan 15 2021
(Magma) [ (n*NthPrime(n+1)) mod NthPrime(n) : n in [1..60]]; // Wesley Ivan Hurt, Apr 23 2021

Crossrefs

Cf. A000040, A117495, A340128.

Sequence in context: A060045 A340051 A000462 * A309942 A282093 A032930

Adjacent sequences: A340646 A340647 A340648 * A340650 A340651 A340652

Keyword

nonn,look

Author

Simon Strandgaard, Jan 14 2021

Status

approved