

A082542


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


3



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
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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)^{(p1)/2)}, where p is the nth odd prime and (a/b) denotes the value of Legendre symbol.  Lekraj Beedassy, Mar 17 2005
a(n) = (A000040(n) OR 3)  1.  Jon Maiga, Nov 14 2018


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, A070750.
Cf. A039702, A071695, A071696.
Sequence in context: A168276 A039722 A237363 * A162776 A032302 A032214
Adjacent sequences: A082539 A082540 A082541 * A082543 A082544 A082545


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, May 02 2003


STATUS

approved



