OFFSET
1,2
COMMENTS
Apart from the term "2", the same as A091177. - Stefan Steinerberger, Dec 29 2007
Numbers n such that the number of distinct residues r in the congruence x^3 == r (mod p) is equal to p where p = prime(n). See A046530. - Michel Lagneau, Sep 28 2016
The asymptotic density of this sequence is 1/2 (by Dirichlet's theorem). - Amiram Eldar, Feb 28 2021
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Integers k such that (prime(k) mod 3) mod 2 = 0. - Gary Detlefs, Dec 06 2011
EXAMPLE
4 is not in the sequence since prime(4)*(2*prime(4) - 1)/3 = 7*(2*7 - 1)/3 = 7*13/3 = 91/3 is not an integer, but 5 is in the sequence since prime(5)*(2*prime(5) - 1)/3 = 11*(2*11 - 1)/3 = 11*21/3 = 11*7 = 77 is an integer. - Michael B. Porter, Sep 28 2016
MAPLE
for n from 1 to 126 do if((ithprime(n) mod 3) mod 2=0) then print(n) fi od; # Gary Detlefs, Dec 06 2011
MATHEMATICA
Union[Table[If[IntegerQ[Prime[n]*(2*Prime[n] - 1)/3], n, {}], {n, 1, 100}]]
pnQ[n_]:=Module[{pn=Prime[n]}, IntegerQ[(pn(2pn-1))/3]]; Select[Range[ 150], pnQ] (* Harvey P. Dale, Oct 02 2011 *)
Sort@ Join[{2}, Select[ Range@ 126, Mod[2*Prime[#], 3] == 1 &]] (* Robert G. Wilson v, Sep 28 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Dec 28 2007
STATUS
approved