A108692 It is known that 4472988326827347533 is a quadratic non-residue for all primes between 3 and 283; sequence gives 4472988326827347533 mod prime(n).

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, 57, 103, 18, 34, 111, 69, 46, 56, 131, 48, 139, 137, 163, 59, 69, 140, 62, 183, 119, 42, 31, 91, 6, 52, 139, 190, 207, 134, 151, 20, 236, 142, 18, 91, 32, 260, 142, 171, 117, 123, 47, 286

Offset

1,2

Comments

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

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

Links

Table of n, a(n) for n=1..68.

Michael John Jacobson, Computational techniques in quadratic fields, Doctor of Science in Computer Science Thesis, University of Manitoba, 1995, 147 pages, (see Table 6.14, p. 133).

Michael John Jacobson Jr. and Hugh C. Williams, New quadratic polynomials with high densities of prime values, Math. Comp. 72 (2003), 499-519 (see Table 4.3, p. 510).

Richard F. Lukes, A very fast electronic number sieve, Doctor of Philosophy in Computer Science Thesis, University of Manitoba, 1995, 253 pages, (see Table 6.8, p. 140).

Dror Speiser, Posting to NMBRTHRY, Jun 18 2005

Index entries for linear recurrences with constant coefficients, signature (1).

Mathematica

Table[Mod[4472988326827347533, p], {p, Prime[Range[70]]}] (* Harvey P. Dale, Dec 07 2020 *)

Prog

(PARI) a(n)=4472988326827347533%prime(n) \\ Charles R Greathouse IV, Jul 03 2013

Crossrefs

Cf. A094849.

Sequence in context: A238761 A261469 A292498 * A157126 A357655 A297703

Adjacent sequences: A108689 A108690 A108691 * A108693 A108694 A108695

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 20 2005

Status

approved