A039702 a(n) = n-th prime modulo 4.

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

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Except for the first term, A100672(n) = (a(n)-1)/2 = parity of A005097. - Jeremy Gardiner, May 17 2008

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A010873.

Cf. A005097, A100672.

Cf. A039701, A039703-A039706, A100672, A005097, A038194, A007652, A039709-A039715.

Programs

Haskell

a039702 = (`mod` 4) . a000040  -- Reinhard Zumkeller, Feb 20 2012

Magma

[p mod 4: p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

Maple

seq(ithprime(n) mod 4, n=1..105); # Nathaniel Johnston, Jun 29 2011

Mathematica

Table[Mod[Prime[n], 4], {n, 105}] (* Nathaniel Johnston, Jun 29 2011 *)
Mod[Prime[Range[100]], 4] (* Vincenzo Librandi, May 06 2014 *)

PARI

a(n)=prime(n)%4 \\ Charles R Greathouse IV, Jun 13 2013

Formula

Sum_k={1..n} a(k) ~ 2*n. - Amiram Eldar, Dec 11 2024