A082542 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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