A271974 Let p = prime(n): if p mod 4 == 1 then a(n) = (1+p)/2 otherwise if p mod 4 == 3 then a(n) = (1-p)/2.

-1, 3, -3, -5, 7, 9, -9, -11, 15, -15, 19, 21, -21, -23, 27, -29, 31, -33, -35, 37, -39, -41, 45, 49, 51, -51, -53, 55, 57, -63, -65, 69, -69, 75, -75, 79, -81, -83, 87, -89, 91, -95, 97, 99, -99, -105, -111, -113, 115, 117, -119, 121, -125, 129, -131, 135, -135, 139, 141, -141, 147, -153, -155, 157, 159, -165, 169, -173, 175, 177, -179, -183, 187, -189, -191, 195, 199, 201, 205

Offset

2,2

Links

Table of n, a(n) for n=2..80.

Dimitris Valianatos, Comments on this sequence, Apr 25 2016

Formula

Product_{n>2} (1-1/a(n)) = (1-1/3)*(1-1/(-3))*(1-1/(-5))*(1-1/7)*(1-1/9)*(1-1/(-9))*(1-1/(-11))*(1-1/15)*(1-1/(-15))*... = (2/3)*(4/3)*(6/5)*(6/7)*(8/9)*(10/9)*(12/11)*(14/15)*(16/15)*... = 1.

So Product_{n>2} (1-a(n)^(-1)) = Product_{n>2}(1-a(n)^(-1))^(-1) = (Product_{n>2}(1-a(n)^(-1)))^k = 1, for every k.

Sum_ {n>2} log(1-1/a(n)) = 0.

Example

For n=11, prime(11) = 31, 31 mod 4 == 3 so a(11) = (1-31)/2 = -15.

Mathematica

If[Mod[#, 4]==1, (1+#)/2, (1-#)/2]&/@Prime[Range[2, 80]] (* Harvey P. Dale, May 09 2017 *)

Prog

(PARI) {forstep(n=3, 1000, 2, if(isprime(n), if(n%4==1, p=(1+n)/2, p=(1-n)/2); print1(n"-> "p", "))); }

Crossrefs

Cf. A039702, A272295.

Sequence in context: A278166 A293990 A247130 * A050824 A323703 A333147

Adjacent sequences: A271971 A271972 A271973 * A271975 A271976 A271977

Keyword

sign

Author

Dimitris Valianatos, Apr 23 2016

Extensions

Corrected and extended by Harvey P. Dale, May 09 2017

Status

approved