A002223 Smallest prime p of form p = 8k-1 such that first n primes (p_1=2, ..., p_n) are quadratic residues mod p.

7, 23, 71, 311, 479, 1559, 5711, 10559, 18191, 31391, 366791, 366791, 366791, 4080359, 12537719, 30706079, 36415991, 82636319, 120293879, 120293879, 131486759, 131486759, 2929911599, 2929911599, 7979490791, 33857579279

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Examples

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

References

• 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. H. Lehmer, E. Lehmer and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp., 24 (1970), 433-451.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• 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.

Links

• A. E. Western and J. C. P. Miller, Tables of Indices and Primitive Roots, Royal Society Mathematical Tables, Vol. 9, Cambridge Univ. Press, 1968 [Annotated scans of selected pages]

Crossrefs

Cf. A045535, A002224, A002225.

Programs

Mathematica

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 *)

Extensions

The Bronson-Buell reference gives terms through 227.

More terms from Don Reble, Sep 19 2001