%I #18 Dec 07 2020 16:59:48

%S 1,2,3,3,8,11,7,15,22,27,3,19,6,28,19,2,11,23,51,63,51,69,74,61,19,2,

%T 57,103,18,34,111,69,46,56,131,48,139,137,163,59,69,140,62,183,119,42,

%U 31,91,6,52,139,190,207,134,151,20,236,142,18,91,32,260,142,171,117,123,47,286

%N It is known that 4472988326827347533 is a quadratic non-residue for all primes between 3 and 283; sequence gives 4472988326827347533 mod prime(n).

%C Suggested by a posting to the Number Theory mailing list by Dror Speiser.

%C a(20509) = a(22206) = a(4498151) = 0; all other values are positive. a(n) = 4472988326827347533 for n > 106704271535495739, while a(106704271535495739) = 16. - _Charles R Greathouse IV_, Jul 03 2013

%H Michael John Jacobson, <a href="http://hdl.handle.net/1993/18862">Computational techniques in quadratic fields</a>, Doctor of Science in Computer Science Thesis, University of Manitoba, 1995, 147 pages, (see Table 6.14, p. 133).

%H Michael John Jacobson Jr. and Hugh C. Williams, <a href="http://www.ams.org/journals/mcom/2003-72-241/S0025-5718-02-01418-7/">New quadratic polynomials with high densities of prime values</a>, Math. Comp. 72 (2003), 499-519 (see Table 4.3, p. 510).

%H Richard F. Lukes, <a href="http://hdl.handle.net/1993/12210">A very fast electronic number sieve</a>, Doctor of Philosophy in Computer Science Thesis, University of Manitoba, 1995, 253 pages, (see Table 6.8, p. 140).

%H Dror Speiser, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;9ed1eff2.0506">Posting to NMBRTHRY</a>, Jun 18 2005

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%t Table[Mod[4472988326827347533,p],{p,Prime[Range[70]]}] (* _Harvey P. Dale_, Dec 07 2020 *)

%o (PARI) a(n)=4472988326827347533%prime(n) \\ _Charles R Greathouse IV_, Jul 03 2013

%Y Cf. A094849.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Jun 20 2005