A002223 - OEIS

%I M4382 N1843 #25 Oct 19 2017 03:13:42

%S 7,23,71,311,479,1559,5711,10559,18191,31391,366791,366791,366791,

%T 4080359,12537719,30706079,36415991,82636319,120293879,120293879,

%U 131486759,131486759,2929911599,2929911599,7979490791,33857579279

%N Smallest prime p of form p = 8k-1 such that first n primes (p_1=2, ..., p_n) are quadratic residues mod p.

%D N. D. Bronson and D. A. Buell, Congruential sieves on FPGA computers, pp. 547-551 of Mathematics of Computation 1943-1993 (Vancouver, 1993), Proc. Symp. Appl. Math., Vol. 48, Amer. Math. Soc. 1994.

%D D. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%D A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots. Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968, p. XV.

%H A. E. Western and J. C. P. Miller, <a href="/A002223/a002223.pdf">Tables of Indices and Primitive Roots</a>, Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968 [Annotated scans of selected pages]

%e 12^2 = 2 mod 71, 28^2 = 3 mod 71, 17^2 = 5 mod 71.

%t np[] := While[p = NextPrime[p]; Mod[p, 8] != 7]; p = 2; A002223 = {}; pp = {2}; np[]; While[ Length[A002223] < 26, If[Union[ JacobiSymbol[#, p] &[pp]] === {1}, AppendTo[pp, NextPrime[Last[pp]]]; Print[p]; AppendTo[A002223, p], np[]]]; A002223 (* _Jean-François Alcover_, Sep 09 2011 *)

%Y Cf. A045535, A002224, A002225.

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_

%E The Bronson-Buell reference gives terms through 227.

%E More terms from _Don Reble_, Sep 19 2001