A340867 a(n) = (prime(n) - a(n-1)) mod 4; a(0)=0.

0, 2, 1, 0, 3, 0, 1, 0, 3, 0, 1, 2, 3, 2, 1, 2, 3, 0, 1, 2, 1, 0, 3, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 3, 2, 1, 0, 3, 0, 1, 2, 3, 0, 1, 0, 3, 0, 3, 0, 1, 0, 3, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 3, 0, 1, 2, 3, 2, 1, 2, 3, 0, 3, 2, 3, 2, 3, 0, 1, 2, 3, 0

Offset

0,2

Links

Table of n, a(n) for n=0..85.

Simon Strandgaard, Visualization

Formula

a(n) = A008347(n) mod 4.

Example

a(1) = ( 2 - 0) mod 4 = 2,
a(2) = ( 3 - 2) mod 4 = 1,
a(3) = ( 5 - 1) mod 4 = 0,
a(4) = ( 7 - 0) mod 4 = 3,
a(5) = (11 - 3) mod 4 = 0.

Mathematica

a[0] = 0; a[n_] := a[n] = Mod[Prime[n] - a[n - 1], 4]; Array[a, 100, 0] (* Amiram Eldar, Jan 30 2021 *)

Prog

(Ruby) require 'prime'
values = [0]
Prime.first(50).each do |prime|
    values << (prime-values[-1]) % 4
end
p values

Crossrefs

Cf. A008347, A339448.

Sequence in context: A159813 A157409 A245960 * A178616 A165252 A371954

Adjacent sequences: A340864 A340865 A340866 * A340868 A340869 A340870

Keyword

nonn

Author

Simon Strandgaard, Jan 24 2021

Status

approved