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A076342
a(n) = A076340(A000040(n)), real part of primes mapped as defined in A076340, A076341.
8
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
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
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Oct 08 2002
STATUS
approved