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

1,1

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

Links

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

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)

Example

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

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 *)

Crossrefs

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

Sequence in context: A055946 A130124 A265417 * A135268 A245619 A131771

Adjacent sequences: A076339 A076340 A076341 * A076343 A076344 A076345

Keyword

nonn,easy

Author

Reinhard Zumkeller, Oct 08 2002

Status

approved