A082542 a(n) = prime(n) + 2 - (prime(n) mod 4).

2, 2, 6, 6, 10, 14, 18, 18, 22, 30, 30, 38, 42, 42, 46, 54, 58, 62, 66, 70, 74, 78, 82, 90, 98, 102, 102, 106, 110, 114, 126, 130, 138, 138, 150, 150, 158, 162, 166, 174, 178, 182, 190, 194, 198, 198, 210, 222, 226, 230, 234, 238, 242, 250, 258, 262, 270, 270, 278

Offset

1,1

Comments

For k > 1: a(k+1) = a(k) if and only if prime(k) == 1 modulo 4 and prime(k+1) = prime(k) + 2, see A071695 and A071696.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000040(n) + A070750(n).

a(n+1) = p + (-1/p) = p + (-1)^((p-1)/2), where p is the n-th odd prime and (-1/p) denotes the value of Legendre symbol. - Lekraj Beedassy, Mar 17 2005

a(n) = (A000040(n) OR 3) - 1. - Jon Maiga, Nov 14 2018

From Amiram Eldar, Dec 24 2022: (Start)

a(n) = A100484(n) - A076342(n).

Product_{n>=1} a(n)/prime(n) = 2/Pi (A060294). (End)

Example

a(2) = 2 because the second prime is 3, and 3 + 2 - 3 = 2.
a(3) = 6 because the third prime is 5, and 5 + 2 - 1 = 6.
a(4) = 6 because the fourth prime is 7, and 7 + 2 - 3 = 6.

Mathematica

Table[Prime[n] + 2 - Mod[Prime[n], 4], {n, 60}] (* Alonso del Arte, Feb 23 2015 *)

Prog

(PARI) vector(60, n, 2 + prime(n) - lift(Mod(prime(n), 4))) \\ G. C. Greubel, Nov 14 2018
(Magma) [2 + NthPrime(n) - (NthPrime(n) mod 4): n in [1..60]]; // G. C. Greubel, Nov 14 2018

Crossrefs

Cf. A000040, A060294, A070750, A076342.

Cf. A039702, A071695, A071696, A100484.

Sequence in context: A168276 A039722 A237363 * A162776 A365925 A032302

Adjacent sequences: A082539 A082540 A082541 * A082543 A082544 A082545

Keyword

nonn,easy

Author

Reinhard Zumkeller, May 02 2003

Status

approved