A076342 a(n) = A076340(A000040(n)), real part of primes mapped as defined in A076340, A076341.

2, 4, 4, 8, 12, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 60, 60, 68, 72, 72, 80, 84, 88, 96, 100, 104, 108, 108, 112, 128, 132, 136, 140, 148, 152, 156, 164, 168, 172, 180, 180, 192, 192, 196, 200, 212, 224, 228, 228, 232, 240, 240, 252, 256, 264, 268, 272

Offset: 1

Author

Reinhard Zumkeller, Oct 08 2002

Keywords

• nonn
• easy

Comments

By definition of the map defined in A076340, A076341: 2->(2,0) and p->((floor(p/4)+floor((p mod 4)/2))*4,2-(p mod 4)) for odd primes p.

Number of solutions to x^2 + y^2 = 1 (mod p). - Lekraj Beedassy, Oct 22 2004

Examples

			A000040(11)=31=(32-1) -> (32,-1), therefore a(11)=32 and A070750(11)=-1.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A070750, A076340, A076341, A082542, A088538.

Programs

Maple

f:= proc(n) local p;
  p:= ithprime(n);
  if p mod 4 = 1 then p-1 elif p mod 4 = 3 then p+1 else 2 fi
end proc:
map(f, [$1..100]); # Robert Israel, Dec 26 2016

Mathematica

a[1] = 2; a[n_] := With[{p = Prime[n]}, p - JacobiSymbol[-1, p]]; Array[a, 60] (* Jean-François Alcover, Feb 01 2018, after Lekraj Beedassy *)
a[n_] := Prime[n] - 2 + Mod[Prime[n], 4]; Array[a, 100] (* Amiram Eldar, Dec 24 2022 *)

Formula

a(n) = p-(-1/p) = p+(-1)^{(p+1)/2} for an odd prime p. {(a/b) stands for the value of the Legendre symbol}. - Lekraj Beedassy, Oct 22 2004

From Amiram Eldar, Dec 24 2022: (Start)

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

a(n) = A100484(n) - A082542(n).

Product_{n>=1} a(n)/prime(n) = 4/Pi (A088538). (End)