OFFSET
0,1
COMMENTS
Same as smallest prime p with property that the Legendre symbol (p|q) = 1 for the first n odd primes q = prime(k+1), k = 1, 2, ..., n, and (p|q) = -1 for q = prime(n+2). - T. D. Noe, Mar 06 2013
EXAMPLE
Let f(p) = list of Legendre(p|q) for q = 3,5,7,11,13,...
Then f(3), f(5), f(7), f(11), ... are:
p=3: 0, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, ...
p=5: -1, 0, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, ...
p=7: 1, -1, 0, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, ...
p=11: -1, 1, 1, 0, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, ...
p=13: 1, -1, -1, -1, 0, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, ...
p=17: -1, -1, -1, -1, 1, 0, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, ...
p=19: 1, 1, -1, -1, -1, 1, 0, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, ...
p=5 is the first list that begins with -1, so a(0) = 5,
p=7 is the first list that begins 1, -1, so a(1) = 7,
p=19 is the first list that begins 1, 1, -1, so a(2) = 19.
MATHEMATICA
f[n_] := Block[{k = 2}, While[ JacobiSymbol[n, Prime[k]] == 1, k++ ]; Prime[k]]; t = Table[0, {50}]; Do[p = Prime[n]; a = f[p]; If[ t[[ PrimePi[a]]] == 0, t[[ PrimePi[a]]] = p; Print[ PrimePi[a], " = ", p]], {n, 10^9}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jun 24 2004
EXTENSIONS
Better definition from T. D. Noe, Mar 06 2013
Entry revised by N. J. A. Sloane, Mar 06 2013
Simpler definition from Jonathan Sondow, Mar 06 2013
STATUS
approved